Exam 22: Inferences About Means

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 among girls aged 9-10,the mean score on a particular aptitude test differs from 72,which is the mean score for boys of the same age.Use the computer output below to draw a conclusion about the girls' scores,using a significance level of 0.05.

A group of researchers wants to determine the mean annual household income for families receiving services at a large community centre.They randomly select ten families and record the following household incomes: $43,955,$42,740,$42,660,$43,800,$43,500,$44,250,$44,340,$40,390,$44,150,$44,200.Decide whether or not the conditions and assumptions for inference with a t-test are satisfied.Explain your answer.

You want to determine if the average gas price in your city has exceeded $1.30 per litre for regular unleaded gasoline.You take a random sample of prices from 8 gas stations ,recording the following prices: $1.33,$1.30,$1.05,$1.29,$1.37,$1.32,$1.30,$1.31.Have the conditions and assumptions for inference been met?

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,constructing the following confidence interval: T-Interval for μ: with 90.00% Confidence,2.3 < μ(grams of fat)< 3.4

Thirty randomly selected students took the calculus final.If the sample mean was 91 and the standard deviation was 11.7,construct a 99% confidence interval for the mean score of all students.

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 : μ = 18 vs : μ < 18

Is the mean weight of female college students still 59.4 kg? To test this,you take a random sample of 20 students,finding a mean of 61.65 kg with a standard deviation of 6.39 kg.Use a significance level of 0.10.

P-value for |t| > 1.44 with 45 degrees of freedom

The average diastolic blood pressure of a group of men suffering from high blood pressure is 96 mm 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: : μ = 96 mm Hg : μ < 96 mm Hg Explain the result of a Type II error.

The principal of a high school randomly selected six students to take an aptitude test.Their scores were: Determine a 90% confidence interval for the mean score for all students.

In the past,the mean running time for a certain type of flashlight battery has been 9.0 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.

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.You take a random sample of prices from 15 gas stations ,recording an average cost of $1.27 and a standard deviation of $0.06.Create a 95% confidence interval for the mean price per litre of gas.

A large software company gives job applicants a test of programming ability,and the mean for the test has been 160 in the past.Twenty-five applicants are randomly selected from one large university and they produce a mean score of 165,with a standard deviation of 13.At a significance level of 0.05,does this indicate that the sample comes from a population with a mean score greater than 160?

Quality control engineers are trying to improve the number of unpopped kernels in their company's microwave popcorn.Changes to the oil have recently been made,so the engineers are testing the hypothesis : μ = 25 against : μ < 25.

P-value for |t| ≥ 2.13 for a sample of size 31

A 99% confidence interval from a sample of size 41

An independent laboratory tests 100 light bulbs,finding that the mean life is 103 hours with a standard deviation of 11 hours.Decide whether or not the conditions and assumptions for inference with a t-test are satisfied.Explain your answer.

A random sample of clients at a weight loss centre were given a dietary supplement to see if it would promote weight loss.The centre reported that the 20 clients lost an average of 15.3 kg,and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±4.5 kg.

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?