Exam 22: Inferences About Means

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline with 95% confidence.You believe that the standard deviation of prices is $0.05.If you wish to achieve a margin of error no larger than $0.02,how many gas stations should you sample?

In 2005,the average final exam score for students in an introductory math course was 72%.Five years later,a teacher wants to perform a hypothesis test to determine whether the average score of students the course has changed from the 2005 mean of 72%.The hypotheses are: : μ = 72% : μ ≠ 72% Explain the result of a Type I error.

Has the introduction of more music download services changed the number of university students that download music for free from the internet? Two years ago,approximately 50,000 university students admitted to downloading music for free from the internet.

Concerned about the high price of gas,you conduct a hypothesis test to determine if the cost of gas in your area has risen above $1.35 per litre.Use the provided computer output to draw a conclusion about the price of gas at a significance level of 0.05.

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.

The football coach at a university randomly selected ten players and timed how long each player took to perform a certain drill.The times (in minutes)were: Determine a 95% confidence interval for the mean time for all players.

Among a sample of 61 students selected at random from a university,the mean number of siblings is 1.5 with a standard deviation of 0.9.Find a 95% confidence interval for the mean number of siblings for all students at this university.

A consumer advocacy group thinks that reduced-fat cookies contain more fat than claimed.They test the hypothesis : μ = 2.5 grams against : μ > 2.5 grams.

In 2005,the average final exam score for students in an introductory math course was 75%.Five years later,a teacher wants to perform a hypothesis test to determine whether the average score of students the course has changed from the 2005 mean of 75%.The hypotheses are: : μ = 75% : μ ≠ 75% Explain the result of a Type II error.

Based on a sample of size 42,a 95% confidence interval for the mean score of all students on an aptitude test is from 57.2 to 64.8.

How many unpopped kernels are left when you pop a bag of microwave popcorn? Each day,quality control personnel take a random sample of 50 bags of popcorn.They pop each bag in a microwave and then count the number of unpopped kernels.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,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.

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,finding a mean fat content of 3.2 grams and a standard deviation of 1.1 grams of fat.Create a 99% confidence interval for the mean grams of fat.

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,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

95% confidence interval with df = 15

A sociologist develops a test to measure attitudes about public transportation.She wishes to compute a 95% confidence interval for the mean score on this test.It is believed that the standard deviation for these test scores will be 21.How many people should be given the test in order to achieve a margin of error of 10?

A 98% confidence interval with 9 degrees of freedom.

Data collected by child development scientists produced the following 90% confidence interval for the average age (in months)at which children say their first word: 10.6 < μ(age)< 13.1.

P-value for t ≤ 1.44 with 45 degrees of freedom

A researcher performs a hypothesis test to test the claim that among car owners in one town,the mean number of kilometres driven per year is greater than 22,540.Use the provided computer output to draw a conclusion about the number of miles driven at a significance level of 0.01.