Exam 20: Inferences About Means

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your fellow students,finding a 95% confidence interval for the mean height of 164.76 to 170.90 cm.

What is the parameter for the t-distribution?

A random sample of 30 households was selected from a particular neighborhood.The number of cars for each household is shown below.Estimate the mean number of cars per household for the population of households in this neighborhood.Give the 95% confidence interval. 2 0 1 2 3 2 1 0 1 4 1 3 2 0 1 1 2 3 1 2 1 0 0 0 5 2 2 1 0 2

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 21 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

You have constructed a 95% confidence interval to estimate the mean number of people downloading music files from the internet using a sample of 150 people.Which of the following statements is/are true? I.A 95% Confidence interval will be wider than a 99% confidence interval. II.Sampling a smaller number of people will increase the margin of error. III.Changing the sample size will change the value of t*.

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.

P-value for $| t |$ > 1.76 with 24 degrees of freedom

A manufacturer produces refrigerators that are claimed to maintain a true mean temperature of 7°C,ideal for certain beverages.The owner of a beverage company wants to conduct a test to determine if the true mean temperature of the refrigerators is different from this value.

Are Canadians getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 190 pounds.Ten years ago,the average weight was 185 pounds.

An 80% confidence interval from a sample of size 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?

In 2009,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 2009 mean of 75%.The hypotheses are: H0: μ = 75% HA: μ ≠ 75% Explain the result of a Type II error.

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. Test of $\mathrm { H } _ { 0 }$ : ? = 72 vs $\mathrm { H } _ { \mathrm { A } }$ : ? ? 72 N Mean StDev t P-value 19 75.88 12.7 1.33 0.20

Alarmed at the rising gas prices in your town,you decide to estimate the average gas price for a litre of regular unleaded gasoline.From your sample of 25 gas stations,you calculate a 90% confidence interval of ($1.33,$1.41).

In 2013,the average duration of long-distance telephone calls originating in one town was $7.2 \text { minutes. }$ A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 2013 mean of $7.2 \text { minutes. }$

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. Test of $\mathrm { H } _ { 0 }$ : ? = 1.35 vs $\mathrm { H } _ { \mathrm { A } }$ : ? > 1.35 N Mean StDev t P-value 22 1.38 0.08 1.759 0.0466

P-value for a right tailed test with a test-statistic of 2.13 from a sample of size 31.

P-value for a right tailed test with a test-statistic of 3.25 from a sample of size 15.

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.

A researcher collected data on the annual salary of doctors in Nova Scotia.He wishes to construct a confidence interval for the mean annual salary.Which of the following is/are true? I.A 98% confidence interval will have a greater chance of including the true mean salary than a 95% confidence interval. II.A 98% confidence interval will be narrower than a 95% confidence interval. III.A 98% confidence interval requires the researcher to take a larger sample.