Exam 7: Inference for Means

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Twelve 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 of shoe they wear in each race is determined at random.All runners are timed and are asked to run their best in each race.The results (in minutes)are given below. Twelve 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 of shoe they wear in each race is determined at random.All runners are timed and are asked to run their best in each race.The results (in minutes)are given below.   Use the sign test for matched pairs to determine if there is evidence that times using Brand 1 tend to be faster than times using Brand 2.Determine which of the following statements is TRUE. Use the sign test for matched pairs to determine if there is evidence that times using Brand 1 tend to be faster than times using Brand 2.Determine which of the following statements is TRUE.

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B

Let n1 represent the sample size of the first group and n2 the sample size of the second group.The t procedures can be used with heavily skewed distributions when n1 + n2 is greater than ____.

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D

A simple random sample should be used for the t procedure when the sample size is small.

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The heights (in inches)of men in the United States are believed to be Normally distributed.The average height of a random sample of 25 American adult men is found to be The heights (in inches)of men in the United States are believed to be Normally distributed.The average height of a random sample of 25 American adult men is found to be   = 69.72 inches with a standard deviation of s = 4.15.What is the standard error of   ? = 69.72 inches with a standard deviation of s = 4.15.What is the standard error of The heights (in inches)of men in the United States are believed to be Normally distributed.The average height of a random sample of 25 American adult men is found to be   = 69.72 inches with a standard deviation of s = 4.15.What is the standard error of   ? ?

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A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below. A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below.   Should a pooled t procedure be used here? Should a pooled t procedure be used here?

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Large sample sizes are needed to find effects of small differences when comparing two means.

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When the underlying assumptions for the use of t procedures are not exactly met,the probability calculations are still valid as long as the data are very close to Normal.

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Two-sample t procedures are more robust than one-sample t procedures.

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The pooled two-sample t procedure is based how many degrees of freedom? (Note: n1 and n2 are the sample sizes of each group. )

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When calculating a one-sample t confidence interval,which level of confidence will give the smallest interval?

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A test of significance is to be carried out on the H0: = 36 against the Ha: < 36,based on data from an SRS selected from a Normally distributed population variable.It was decided to use a level of significance of = 0.02 to decide whether or not to reject the null hypothesis.The sample data produced a standard deviation of s = 15.6 based on 12 sample values.What values of A test of significance is to be carried out on the H<sub>0</sub>: <font face=symbol></font><font face=symbol></font>= 36 against the H<sub>a</sub>: <font face=symbol></font> < 36,based on data from an SRS selected from a Normally distributed population variable.It was decided to use a level of significance of <font face=symbol></font> = 0.02 to decide whether or not to reject the null hypothesis.The sample data produced a standard deviation of s = 15.6 based on 12 sample values.What values of   would lead to the rejection of H<sub>0</sub>? would lead to the rejection of H0?

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A study was conducted to determine if taking a popularly advertised herbal supplement will result in weight loss in obese males.A random sample of clinically obese males was obtained.Each subject was weighed before taking the supplement and again after 60 days using the supplement.Subjects were told not to alter their diet in any way during the study period.The following table shows the observed results for the six subjects. A study was conducted to determine if taking a popularly advertised herbal supplement will result in weight loss in obese males.A random sample of clinically obese males was obtained.Each subject was weighed before taking the supplement and again after 60 days using the supplement.Subjects were told not to alter their diet in any way during the study period.The following table shows the observed results for the six subjects.   What are the appropriate hypotheses to use in this case to determine if the herbal supplement is effective in achieving weight loss in obese males? What are the appropriate hypotheses to use in this case to determine if the herbal supplement is effective in achieving weight loss in obese males?

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When performing a two-sample t procedure,which of the following methods will help determine the degrees of freedom?

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When performing a t procedure,it is best to look at the data first and then determine if you should do a one-sided or two-sided test.

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A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below. A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below.   What is the alternative hypothesis being tested? What is the alternative hypothesis being tested?

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Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces.Net weights actually vary slightly 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 Ha: < 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 ounces with a standard deviation of s = 0.24 ounces.Determine which of the following statements is true,regarding the decision the representative would make.

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The probability calculations from a t procedure are valid if there are outliers in the data as long as the sample size is large and the data are Normal.

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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 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 <font face=symbol></font> = 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.What is the appropriate alternative hypothesis in this situation? = 47.4 mL/kg/min with a standard deviation of s = 5.3 mL/kg/min.What is the appropriate alternative hypothesis in this situation?

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Suppose a simple random sample size of n is drawn from an appropriately normal population.What degrees of freedom should be used to perform a one sample t procedure?

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The hypotheses H0: = 10 versus Ha: 10 are examined using a sample of size n = 18.The one-sample t statistic has the value t = -2.05.Between what two values does the P-value of this test fall?

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