Exam 7: Inference for Means

Suppose you are interested in determining if the average amount of money that students spend on food at your university per day is greater than $30.You randomly choose 25 students from your campus and calculate that the mean amount of money spent per day is $18.01 with a standard deviation of $2.22.Would you use a one-sided or two-sided test for this problem?

Which of the following cannot be used to check the assumptions for the t procedure?

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz.Net weights slightly vary from bag to bag.Assume net weights are Normally distributed.A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H₀:  = 14 versus H_a:  < 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.Assume the standard deviation for the distribution of actual net weights for bags of tortilla chips of this brand is  = 0.25.At the 5% significance level,what is the power of our test when,in fact, = 13.8 oz?

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students. Would the null hypothesis be rejected at the .05 significance level after removing the second observation (value = 100)?

We are interested in testing a null hypothesis about a population mean  being equal to a specified value using a simple random sample of size 25.In the past the population variable has shown a slight tendency to non-Normality (slight skewness but no strong outliers).Why can we safely use a t procedure in this testing situation?

A simple random sample of six patients over the age of 65 is being used in a blood pressure study.The standard error of the mean blood pressure of these six men was 22.8.What is the standard deviation of these six blood pressure measurements?

A simple random sample of 100 postal employees 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 = 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 H₀:  = 7.5 versus H_a:   7.5.A one-sample t test will be used.What are the appropriate degrees of freedom for this test?

Ten couples are participating in a small study on cholesterol.Neither the man nor the woman in each couple is known to have any problems with high cholesterol.The researcher conducting the study wishes to use the sign test for matched pairs to determine if there is evidence that the cholesterol level for the husband tends to be higher than the cholesterol level for the wife.The cholesterol measurements for the 10 couples are given below. What is the (approximate)value of the P-value?

P-values for the sign test for matched pairs are calculated using which distribution? (Note: n is the number of trials where the difference is not zero. )

A random sample of 20 observations produced a sample mean of = 92.4 and s = 25.8.What is the value of the standard error of ?

A study was done to determine whether there is a difference in the amount of time (in hours)that graduate students versus undergraduate students spend on the Internet per day.The results of the analysis are shown below. Is there a significant difference in the amount of time that graduate and undergraduate students spend on the Internet?

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students. If we remove the second observation (value = 100),we could test the hypothesis using a ____ .

Scores on the math section of the SAT are believed to be Normally distributed.The scores of a simple random sample of five students who recently took the exam are 550,620,710,520,and 480.What is a 95% confidence interval for ,the population mean score on the math section of the SAT?

The pooled two-sample t procedure can be used when ______.

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students. Suppose you were to remove the second observation (value = 100),would a t procedure be appropriate for these data?

To estimate ,the mean salary of full professors at American colleges and universities,you obtain the salaries of a random sample of 400 full professors.The sample mean is $73,220 and the sample standard deviation is $4400.What is a 99% confidence interval for the mean ?

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  = 45 mL/kg/min.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 = 47.4 mL/kg/min with a standard deviation of s = 5.3 mL/kg/min.Based on these data,what is the 98% confidence interval estimate for the mean oxygen uptake for the population from which the sample of students was selected?

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  = 45 mL/kg/min.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 = 47.4 mL/kg/min with a standard deviation of s = 5.3mL/kg/min.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?

A simple random sample of 100 postal employees 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 = 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 H₀:  = 7.5 versus H_a:   7.5.A one-sample t test will be used.Suppose the mean and standard deviation obtained were based on a sample of size n = 25 postal workers rather than 100.What do we know about the value of the P-value?

Do students tend to improve their SAT Mathematics (SAT-M)scores the second time they take the test? A random sample of four students who took the test twice received the following scores. Assume that the change in SAT-M score (second score - first score)for the population of all students taking the test twice is Normally distributed.Suppose we do not believe that students tend to improve their SAT-M scores the second time they take the test.Based on a 90% confidence interval,we wish to test H₀:  = 0 versus H_a:   0 at the 5% significance level.Determine which of the following statements is true.