Statistics Final – Flashcards
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T/F a statistic is a numerical summary of a population
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false, sample taken from population
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T/F the standard deviation can be negative
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false
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if a data set with more than one standard observation has a standard deviation of s=0, what does that imply about the data set?
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they all have the same value
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T/F the r^2 value can measure direction & strength
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false, not direction
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T/F the r value can be negative
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true
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T/F A sample of n subjects from a population is one in which each possible sample of that size has the same chance of being selected.
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false
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T/F P(A)= 1-P(Ac)
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true
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P(AUB)-P(A^B)= P(A)+P(B)
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false, should be P(AUB) plus P(A^B)
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T/F If A & B are two events, then P(A^B)=P(A) + P(B)
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false, multiply P(A) and P(B)
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T/F The proportion of occurrences of a random event approaches the probability of that event occurring as the number of trials approaches infinity
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true
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T/F a binomial experiment is an experiment with a independent trials, each trial has two outcomes.
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false
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T/F For a probability distribution, 0<(or equal to) P(X=x) for all possible values of x.
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false
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T/F in a game involving monetary prizes, that game is called a fair game if the expected value of that game is 0
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true
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T/F the cumulative probability is the probability of an observation falling above a certain value.
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false, falling below
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T/F the data distribution is the distribution of the sample data
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true
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T/F the sampling distribution is the probability distribution for a given statistic coming from a random sample.
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true
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T/F the sampling distribution of the sample proportion Xbar approaches an approximately normal distribution as the sample size n increases.
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false, sample mean
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A historian woman wants to estimate the average age at marriage of women in New England. Within her state archives she finds 2500 marriage records. the average age of the women is 24.1. using the appropriate statistical method, she estimates that the avg. was between 23.5 and 24.7 years. 1) identify the population 2)identify the sample
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population: all the married women in New England sample: 2500 married women
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In the 2008, general society survey, respondents answered the question "How many children have you had?" the results were: # of children- 0,1,2,3,4,5,6,7 & Frequency- 521,323, 524, 344,160,77,30,41 1) what is the variable? 2)is it categorical/quantitative? 3) discrete or continuous? 4) find mean,median,mode
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1) # of children 2) quantitative 3)discrete 4) mean: 1.928 median: 2.000 mode:2.00
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the data below shows the # of miles that adults drive to work in milledgeville 10,12,8,5,4,6,5,9,10,5 1) find the range 2) find the st. deviation 3) Would you expect for # of miles that adults drive in Atlanta to have a smaller or larger or about the same st. dev.? why?
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1) 12-4= 8 miles 2) 2.757 3) larger, bc some people live in the city and are very close, & some are in the suburbs and have to drive further.
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The height of women are normally distributed with a mean of 64.5 inches and a standard deviation of 2.1 inches. 1) find 1 st. dev. away from mean 2) find 2 st. dev. away from mean 3)find 3 st. dev. away from mean 4) According to empirical rule, write the percentage of data that fall in the intervals above. 5) Would a woman's height of 72 inches(6 ft) be considered unusual? Why or why not?
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1) 62.4 and 66.6 inches 2)60.3 and 68.7 inches 3) 58.2 and 70.8 inches 4) 72-64.5/ 2.1= 3.75 5) yes, she'd be considered an outlier bc she falls within 3.571 st. deviations from the mean, which is greater than 3.
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Suppose you flip a coin 3 times and get 0 heads. does this mean the prob. of getting heads is 0?
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No, it means that you haven't flipped the coin enough times to get a accurate probability
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Suppose you flip a coin 3 times 1) write sample space 2) what's the prob. of getting 1 head on 3 coin flips? 3) what's prob. of getting 0 heads on 3 coin flips? 4) what's prob. of getting at least 1 head on 3 flips? 5) suppose the coin isn't a fair coin. instead, the coin is weighted & lands on heads 90% of the time. -what's the prob. of getting 0 heads on 3 flips? -what's prob. of getting at least 1 head on 3 flips?
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1) HHH,HHT,HTH,HTT,THH,THT,TTH,TTT 2) 3/8=.375 3) 1/8= .125 4)7/8= .875 5) (.10)^3= .001 1-.001=.999
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table describes smoking habits of 119 asthma sufferers. nonsmoker occasional regular heavy Men: 370, 45, 61, 39 Women: 443, 39,84, 38 1) find the prob. that a randomly selected person is a heavy smoker 2) Find the prob. that randomly selected person is a heavy smoker OR a man 3) Find the prob. that a randomly selected is a heavy smoker AND a man 4) Find the prob. that a randomly selected person is a heavy smoker given it is a man. 5) Are the events "heavy smoker" and "man" ind.?
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1) .069 2) .494 3).035 4) .076 5) No
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In one town, 42% of all voters are democrats. If two voters are randomly selected for a survey: 1) find the prob. that neither of them is a democrat 2) find the prob. that at least 1 is a democrat
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1) (.58 X .58)= .3364 2) 1-.3364= .6636
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Table shows the soft drink preferences of people in different age groups. Cola(c) Root Beer(r) lemon-lime(L) under 21(U): 40 25 20 btw 21 & 40(B): 35 20 30 over 40 (O): 20 30 35 1) find p(C) 2) P(C/U) 3) describe the difference between questions 1 & 2
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1) (40+35+20)/255=.373 2) 40/85=.471 3) 1 is asking for the prob. that cola is given person's preference and 2 is asking the prob. that cola is preferred, given that the person is under 21.
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The # of golf balls ordered by customers of ABC pro shop has the following prob. distribution. x [ 3 [ 6 [ 9 [ 12 [ 15 p(x)[ .14 [ .11 [ .36 [ .29 [ .10 1) find the mean of this prob. distribution 2) you can expect Bill, a customer at ABC, will order___ golf balls on his next order. 3) you can expect that any ABC customer will order___ golf balls on his/her next order. 4) You can expect that, after taking orders from many customers, you will need to order on average _____ golf balls per customer 5) Find the st. deviation of this prob. distributiom
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1) x= 9.3 2) 9.3 3) 9.3 4) 9.3 5) Sx= 3.49
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About 40% of the general population donate time and energy to community projects. Suppose 15 people have been randomly selected from a community & each asked whether he or she donates time & energy to community projects. Let x be the # who donate time and energy to community projects. 1) x is a binomial random variable, which means that there are only 2 possible outcomes for each trial. What are the 2 possible outcomes for each trial? 2) Specify the values for n and p 3) Find the prob. that 3 of the 15 randomly selected people donate time and energy to community projects 4) Find the prob. that less than 3 of the 15 donate time and energy to community projects. 5) Find the probability that more than 3 of the 15 donate time and energy to community projects
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1) -people who donate time & energy to community projects - people who don't donate time & energy to community projects 2) n=15 p= .40 3) p(x= 3) binomialpdf(15,.40,3) = .063 4) p(x3) 1-binomialcdf(15,.40,3)= .909
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16% of all individuals are left handed writers. 1) in a class of 20 students, what is the expected number of left-handed writers? 2) What is the St. Deviation? 3) If none of the students in the class are left-handed, is that considered unusual? why or why not?
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1) (.16 x 20)= 3.2 2) Sx= square root(3.2)(8.4)= 1.64 3. No, this isn't unusual. 0 falls within 3 st. deviations of the mean.
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Farmers often sell fruits and vegetables at roadside stands during the summer. One such road side stand has a daily demand for tomatoes that is approximately normally distributed with a mean of 465 tomatoes and a st. deviation of 30 tomatoes. Today, the farmer set a goal to sell more than 500 tomatoes. What's the probability that he will reach this goal? -draw curve,label, and shade (don't answer here see test) 1) Find the appropriate z-score 2) Answer the question addressed
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1) z= 500-465/30= 1.17 2) normalcdf(1.17,5)= .121
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Assume that the salaries of elementary school teachers in the U.S. has a mean of $32,000 and a standard deviation of $3000. Find the probability that a elementary school teacher's salary is less than $34,500. -draw curve,label, and shade (don't answer here see test) 1) find appropriate z-score 2)answer the question addressed
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1) z= 34500-32000/3000= .83 2) normalcdf(-5,.83)=.7967
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Assume that the salaries of elementary school teachers in the U.S. has a mean of $32,000 and a standard deviation of $3000. What salary would place an elementary school teacher in the top 5% of all elementary school teachers' salaries? -draw curve,label, and shade (don't answer here see test) 1) find appropriate z-score 2)answer the question addressed
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1) z-score= .95 2) invnorm(.95,32000,3000)= $36, 934.56
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Assume that the salaries of elementary school teachers in the U.S. has a mean of $32,000 and a standard deviation of $3000. If 100 teachers are randomly selected,find the prob. that their mean salary is greater than $32,500. -draw curve,label, and shade (don't answer here see test) 1) find appropriate z-score 2)answer the question addressed
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1) z-score= 1.67 2)normalcdf(1.67,5)=.0475
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A study in Applied Psycho linguistics measured language skills of young children. They found that the sentence complexity scores of 65 low-income children had a mean of 7.62 and a st. deviation of 8.91. 1) Draw a graph and shade appropriately in order to find a 90% confidence interval for the mean sentence complexity score of low-income children. (see Test) Find a 90% confidence interval. 2) Interpret this interval
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1) invnorm(.05, 7.62, 8.91/square root(65)=5.802 invnorm(.95, 7.62, 8.91/square root (65)= 9.438 answer: (5.802, 9.438) 2) We can be 90% confident that the mean lies between the lower bound and upper bound of the confidence interval
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ABC juice bottling company had some customer complaints that their juice bottles had less juice in them than the advertised amount. The amounts (in ounces) of juice in 8 randomly selected juice bottles are: 15.0 15.9 15.3 15.3 15.5 15.9 15.9 15.0 1) draw a graph and shade appropriately in order to find a 98% confidence interval for the mean amount of juice in all such bottles.(see test) Find a 98% confidence interval. 2) What is the effect of increasing the sample size on the width of the confidence interval?
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1) t-score=2.998 2.998 X .3882193783/square root(8)+ 15.475= 15.886 -2.998 X .3882193783/square root(8)+ 15.475= 15.064 answer: (15.064, 15.886) 2) as the sample size increases, the width decreases.
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Find the z-score corresponding to a a) 94% confidence level with 7 observations b) 99.9% confidence level with 20 observations c) 80% confidence level with 5 observations d) 19% confidence level with 50 observations
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a) invnorm(.03,0,1)= 1.88 b) invnorm(.005,0,1)= 2.58 c) invnorm(.1, 0,1)= 1.28 d) invnorm(.405, 0, 1)= .2404
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Find the t-score corresponding to a a) 95% confidence level with 7 observations b) 92.3% confidence level with 20 observations c) 71.5% confidence level with 5 observations d) 99% confidence level with 50 observations
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a) invt(.95,6)= 1.94 b) invt(.923, 19)= 1.48 c) invt(.715,4)= .618 d) invt(.99,49)= 2.405
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True or False: The t-distribution is equivalent to the normal distribution when the number of observations is at least 30.
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True
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True or False: The t-distribution is used to find confidence intervals for population proportions.
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False, for population means
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The margin of error with 95% confidence for a certain population mean estimate is 0.35318 and the standard deviation is 0.45947. If the corresponding t-score is 2.30600, how many observations were there?
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n=9
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Two data sets have the same standard deviation and mean but one of the data sets has 19 observations while the other has 18. If the 95% confidence interval is constructed for the population mean for each data set, which confidence interval will be wider? Explain.
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18 observations because the smaller the observation, the wider the interval
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8 Two data sets have the same standard error and a confidence interval for the population proportion is to be constructed for each data set. For one of the data sets, a 95% confidence interval is constructed and for the other data set, a 96% confidence interval is constructed. Which of the two resulting confidence intervals is wider? Explain.
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96% because a increase in confidence level, the wider the interval
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Two data sets, one with 19 observations and the other with 14 observations, have the same standard deviation. The 95% confidence interval for the population mean is constructed for the data set with 19 observations and the 90% confidence interval for the population mean is constructed for the data set with 14 observations. Which of the two resulting confidence intervals is wider? Explain.
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19 observations and 95%
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You conduct a survey of 40 random students at Georgia College to see who they will vote for during the upcoming student body president election. Of the 40 surveyed, 16 plan to vote for R. Deschain. Construct the 90% confidence interval for the proportion of the student body that will vote for R. Deschain. (HINT: use 1-propzint)
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[.2725, .5275]
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The percentage of Americans that favored nuclear power in 1990 was 51%.1 You want to know whether or not public opinion on nuclear energy has improved since 1990. To do this, you randomly survey 250 Americans in 2014. Of the 125 surveyed, 85 are in favor of nuclear energy. a) What are the null and alternative hypotheses? b) Does this hypothesis involve a left-tail test, a right-tail test, or a two-tailed test? c) What is the P-value? d) Does your data suggest that public opinion increased on this issue since 1990?
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a) null- Ho: p= .51 alternative- Ha: p>.51 b) left tail c) 7.146 X 10^-5 d) yes, because it is less than .05 so you accept the alternative
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Consider the the percentage of Americans that favored nuclear power in 1990 was 51%.1 You want to know whether or not public opinion on nuclear energy has improved since 1990. To do this, you randomly survey 250 Americans in 2014. instead of examining whether or not public opinion has increased, say you want to know whether or not public opinion has changed at all (increased or decreased). a) What are the null and alternative hypotheses? b) Does this hypothesis involve a left-tail test, a right-tail test, or a two-tailed test? c) What is the P-value? d) Does your data suggest that public opinion changed on this issue since 1990?
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a) Ho: p=.51 Ha= p not = .51 b) two-tailed c) p= 1.44e^-4 d) yes, it's not equal to .05
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In the United States, 53% of Hispanic Americans have blood type O+.2 You randomly sample the blood types of 80 Hispanics in Georgia and find that 39 have blood type O+. You want to know whether or not there are fewer Hispanics in Georgia that have blood type O+. a) What are the null and alternative hypotheses? b) Does this hypothesis involve a left-tail test, a right-tail test, or a two-tailed test? c) What is the P-value?
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a) Ho: p=.53 Ha: p< .53 b) right tail c) p= .776
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A friend believes that your 6-sided die is unfair and that even numbers are rolled more often than odd numbers. a) what is null and alternative? b) If you roll the die 500 times and an even number is rolled 273 of those times, is there evidence supporting your friends claim? Explain.
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a) Ho: p=.5 Ha: p>.5 b) p=.0198 No, because p<.5 so you reject the null and accept the alternative.
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A 2002 study found that the average score on the quantitative section of the Graduate Record Examination (GRE) General Test between years 1994 and 1997 was 558.3 You wish to know whether or not the average in 2014 differs from 558. To do this, you randomly gather 200 quantitative section GRE scores in 2014. The mean of these scores is 561 with standard deviation 24.01. a) What is the null and alternative hypotheses? b) Does this hypothesis involve a left-tail test, a right-tail test, or two-tail c) What is the P-value? d) Is there statistically significant evidence that the GRE quantitative average in 2014 is higher than 558?
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Mo= 558 Ma not = 558 two-tailed test Se= 24.01/ square root(200) = 1.69776 t-score= 561-558/1.69776 = 1.7670 p-value: tcdf( 1.7670, infinity, 199)= .03938 tcdf( neg. infinity, -1.7670, 199)= .0786 P> .05 so keep Ho.
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In Franklin's tower, there hangs a bell. Children race to the top of the tower to ring the bell. Up to 2013, the average time to reach the bell has been 19 seconds. In 2014, 213 children have raced to the bell. Their average time to reach the bell was 18.89 seconds with standard deviation 0.32 seconds. Is there statistically significant evidence suggesting that the speed of the children in 2014 is slower than the average time up to 2013?
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Mo= 9 Ma > 9 right tail t= .912 P= 1.98 P> .05 so yes it is slower.
