Exam 20: Inferences About Means

A researcher wants to estimate the mean cholesterol level of people in his city.He sets up a walk-in clinic,and measures the cholesterol of 85 people,finding a mean level of 224 and a standard deviation of 8.Have the conditions and assumptions for inference been met?

The principal of a high school randomly selected 30 students to take a math test.Of the 30 students who wrote the test,19 scored more than 75%,4 scored exactly 75%,and 7 scored below 75%.Perform a sign test to determine if the median score is greater than 50% using a 1% level of significance.

The average diastolic blood pressure of a group of men suffering from high blood pressure is $96 \mathrm {~mm} \mathrm { Hg } .$ During a clinical trial,the men receive a medication which it is hoped will lower their blood pressure.After three months,the researcher wants to perform a hypothesis test to determine whether the average diastolic blood pressure of the men has decreased.The hypotheses are: H0: ? = $96 \mathrm {~mm} \mathrm { Hg }$ HA: ? < $96 \mathrm {~mm} \mathrm { Hg }$ Explain the result of a Type II error.

Under what name did William S.Gosset publish his work on the t-distribution?

A sociologist develops a test to measure attitudes about public transportation,and 27 randomly selected subjects are given the test.Their mean score is 76.2 and their standard deviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects.

A researcher performs a hypothesis test to test the claim that for a particular breed of dog,the mean weight of an adult dog is less than 18 kg.Use the given computer output to draw a conclusion about the mean adult dog weight for this breed at a significance level of 0.05. Test of $\mathrm { H } _ { 0 }$ : ? = 18 vs $\mathrm { H } _ { \mathrm { A } }$ : ? < 18 N Mean StDev t P-value 21 17.883 0.212 -2.53 0.01

In the past,the mean running time for a certain type of flashlight battery has been $9.0 \text { hours. }$ The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

To determine the mean number of unpopped kernels in your favorite brand of microwave popcorn,you pop a random sample of 50 bags of popcorn and construct of 98% confidence interval of (12.5,15.4).

A researcher wants to determine if the average cholesterol level in his city is different from the national average of 195.Use the provided computer output to draw a conclusion about the cholesterol levels in the researcher's city,at a significance level of 0.10. Test of $\mathrm { H } _ { 0 }$ : ? = 195 vs $\mathrm { H } _ { \mathrm { A } }$ : ? ? 195. N Mean StDev t P-value 50 198 12 1.768 0.0833

A quality control manager at a bottling plant wishes to know if the median amount of juice in their 473 mL bottles actually falls below 473 mL.The amounts of juice in 24 randomly selected juice bottles are measured.Of the 24 bottles,14 contained less than 473 mL and 10 contained more 473 mL.Perform a sign test to determine if the median amount is less than 473 mL.Use a 10% level of significance.

A laboratory wishes to compute a 95% confidence interval for the mean amount of cholesterol,in milligrams,in chicken eggs.They believe the population standard deviation to be 40 milligrams.How many eggs should they use if they want a margin of error of 20 milligrams?

98% confidence interval with df = 20

A 95% confidence interval from a sample of size 200

Consider a right skewed distribution.What is the shape of the sampling distribution for the sample mean based on samples of 1 observation?

The principal of a high school randomly selected 30 students to take a math test.Of the 30 students who wrote the test,18 scored more than 75% and 12 scored below 75%.Perform a sign test to determine if the median score is greater than 50% using a 5% level of significance.

A consumer advocacy group thinks that reduced-fat cookies contain more fat than claimed.They test the hypothesis $\mathrm { H } _ { 0 } : \mu = 2.5$ grams against $\mathrm { H } _ { \mathrm { A } } : \mu > 2.5$ grams.

P-value for t ≥ 1.76 with 24 degrees of freedom

In the past,the mean battery life for a certain type of flashlight battery has been $9.5 \text { hours. }$ The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean battery life has increased as a result.The hypotheses are: H0 : ? = 9.5 hours HA: ? > 9.5 hours Explain the result of a Type II error.

A laboratory wishes to compute a 95% confidence interval for the mean amount of cholesterol,in milligrams,in chicken eggs.They believe the population standard deviation to be 15 milligrams.How many eggs should they use if they want a margin of error of 10 milligrams?

A 98% confidence interval with 9 degrees of freedom