Statistics test 3

Suppose we wish tomtest the hypothesis H0:mu=10 versus Ha:mu< 10, where mu represents the mean age of non-highschool aged children who are members of a large gymnastics club in a metropolitan area. Assume age follows a normal distribution with std. Deviation of a population=2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be xbar=8.76.

The time needed for college students to complete a certain paper and pencil maze follows a Normal Distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time (mu) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Suppose if takes the nine students an average of xbar=32.05 seconds with a standard deviation of 3.2 seconds to complete the maze. At the 1% significance level! what can you conclude?

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with Std. Deviation of a population of 30. A random sample of 25 bulbs put on test produced a sample mean lifetime of xbar=1038. Based on the above information, the 95% confidence interval estimate for the mean lifetime, μ, is:

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. net weights actually vary slightly from bag to bag. Assume net wrights are normally distributed. A representative of a consumer advocate group wishes to see of there is any evidence that the mean weight is less than advertised and so intends to test the hypothesis H0: μ<14. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of 13.88 oz with a standard deviation of s=0.24 oz.

12 runners are asked to run a 10- kilometer race on each of two consecutive weeks. In one of the races the runners wear one brand of shoe and in the other a different brand. The brand shoes they wear in which race is determined at random. All runners are timed and are asked to run their best in each race. The results (in minutes) are below:

What is a more powerful test than a sign test?

A study was to be undertaken to determine if a particular training program would improve physical fitness. An SRS of 31 university students was selected to be enrolled in the fitness program. One important measure of fitness is maximum oxygen uptake. Measurements of oxygen uptake in untrained individuals are known to follow a Normal distribution with a mean of μ=45. The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects. The measurements made on the subjects coming into this study produced a mean of xbar=47.4 with a std. Deviation of s=5.3

Researcher compared two groups of competitive rowers: a group of skilled rowers and a group of novices. The researchers measured the angular velocity of each subjects right knee. The sample size n, the sample means, and the sample standard deviations for the two groups are given below...

A fire insurance company wishes to study the amount of fire damage in major residential fires. The data they collected from a simple random sample of fires in the past six months are shown below... The fire chief wishes to estimate the mean amount of damage with a 95% confidence interval

The candy company that makes M&M's claims that 10% of the M&M's it produces are green. Suppose that the candies are packaged at random in large bags of 200 M&M's. When we randomly pick a bag of M&M's we may assume that this represents a simple random sample of size n=200. Suppose we wish to test Ho: p=.10 versus Ha:p doesn't equal .10. If your bad has 32 green M&M's what can you conclude?

After once again losing a football game to the college's archival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.

At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. Has the proportion of freshmen in the bottom third of their high school class significantly decreased from 1993 to 1997?

Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed to simply compensate for the lost support from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university we're asked whether or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table...

A simple random sample of 100 postal employee is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was xbar=7 years with a standard deviation of s=2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are Ho:μ=7.5, Ha:μ not equal to 7.5.

Suppose we want to determine if students tend to improve their SAT score the second time they take the test. Based on the confidence interval previously calculated, we wish to test Ho:μ=0 versus Ha:μ>0 at the 5% significance level. Determine which of the following statement sets of p-values match the results for a 1-sample t and a sign test (conduct each test and match the respective p- values below

Matched pairs t procedures (when you combine two distributions into one and test for a mean difference=0 as the null hypothesis) are for use on subjects that are

An instructor is teaching two sections of the same basic statistics course. The instructor is giving the same exams, homework assignments, and quizzes I both sections. Which test should be used to determine if there is a difference in the academic performance between the two course sections?

16 people volunteered to be part of an experiment. All 16 people were Caucasian, between the ages of 25 and 35 and were supplied with nice clothes. 8 of the people were male and 8 were female. The question of interest in this experiment was whether females receive faster service at restaurants than males. Each of the eight male participants was randomly assigned a restaurant, and each of the eight females was randomly assigned to one of these same eight restaurants. One Friday night all 16 people went out to eat, each one alone. The male and female assigned to the same restaurant would arrive within 5 minutes of each other, with the order determined by flipping a coin (male first or female first). Each person the ordered a similar drink and a similar meal. The time until the food arrived at the table was recorded. μ=0

A study was to be undertaken to determine if a particular training program was significantly related to physical fitness. An SRS of 31 university students was selected to be enrolled in the fitness program. One important measure of fitness is maximum oxygen uptake. Measurements of oxygen uptake in untrained individuals are known to follow a Normal Distribution with a mean of μ=45. The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects. The measurements made on the subjects coming into this study produced a mean of xbar=47.4 with a standard deviation of s=5.3.

If the 98% confidence interval were determined to be (45.2, 49.6) an interval, which may or may not be correct, what would the researchers conclude?

If the level of confidence were changed to 95% what would happen to the size of the confidence interval (i.e. Size of the marginof error) and the p-value?

A researcher is interested in determining if the model used for the distribution of main economic concerns in the year 2003 for residents in a certain county can still be used in the year 2004. A sample of 370 residents from that county was surveyed in 2004. The following table displays the model for the distribution of economic concerns for the year 2003 and the observed number of sampled respondents in the survey for the same economic concerns for the year 2004

When testing the null hypothesis when doing chi squared...

Could mud wrestling be the cause of a rash contracted by University of Washington students in the spring of 1992? Two physicians at the University of Washington student health center wondered this when one male and six females complained of rashes after participating in a mud-wrestling event. Questionnaires were sent out to all students in the residence halls who participated in the event. The results by gender are summarized in the following table:

Central middle school has calculated a 95% confidence interval for the mean height (μ) of 11 year old boys at their school and found it to be 56 +/- 2 inches. Which of the following could be the 90% confidence interval based on the same data?

When we state the alternative hypothesis to look for a difference in a parameter in any direction, we are doing a

The ____ the p value the stronger the evidence against the null hypothesis provided by the data

When performing significance tests at alpha level if the p value obtained is ___, the null hypothesis will not be rejected

If the p value is as small or smaller than a specified value of alpha, then the data are ____ significant

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all season tires traveling at 90 kn/hr, the mean stopping time in fresh snow is known to be 215 meters with a standard deviation of σ=2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of 9 snow tires for the manufacturer on a snow-covered track. The tests resulted in a mean stopping distance of xbar =212.9 meters.

The nicotine content in cigarettes of a certain brand is Normally distributed with a σ=.01 milligrams. The brand advertises that the mean nicotine content of their cigarettes is μ=1.5 but measurements on a random sample of 100 cigarettes of this brand gave a mean of xbar=1.53. Is this evidence that the mean nicotine content is actually higher than advertised?

The survey of study habits and attitudes is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 follow approximately a normal distribution with mean 115 and standard deviation 25. You suspect that incoming freshmen at your school have a mean μ, which is different from 115 because they are often excited yet anxious about entering college. You give the SSHA to 25 incoming freshmen and find their mean score to be 116.2.

Suppose we wish to test the hypothesis H0: μ=10 versus Ha: μ<10, where μ represents the mean age of non-high school aged children who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with σ=2. Random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be xbar=8.76