Exam 22: Inferences About Means

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.

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 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.

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.

How tall is the average student on your campus? To determine this,you measure the height,in centimetres,of a random sample of 9 of your fellow 100 students and calculate the following confidence interval with 95% confidence: 155.72 < μ(height)< 181.20

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 100 fellow students,finding a mean height of 166.6 cm and a standard deviation of 5.64 cm.Have the conditions and assumptions for inference been met?

Is the mean lifetime of particular type of car engine greater than 350,000 km? To test this claim,a sample of 23 engines is measured,yielding an average of 365,000 km and a standard deviation of 18,500 km.Use a significance level of 0.01.

How much fat do reduced fat cookies typically have? You take a random sample of 50 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.Have the conditions and assumptions for inference been met?

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 100 fellow students,finding a 95% confidence interval for the mean height of 164.76 to 170.90 cm.

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

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

90% confidence interval with df = 4.

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 237 milligrams with s = 14.0 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Marc wants to know if the mean age of the prison population in his city is less than 26 years.He obtains a random sample of 25 prisoners,and finds a mean age of 24.4 years and a standard deviation of 9.2 years.At a significance level of 0.05,what is his conclusion?

How many unpopped kernels are left when you pop a bag of microwave popcorn? Quality control personnel at Yummy Popcorn take a random sample of 50 bags of popcorn.They pop each bag in a microwave and then count the number of unpopped kernels.The following interval is produced: T-interval for μ : with 99% Confidence,11 < μ(unpopped)< 25

A manufacturer claims that the mean amount of juice in its 500 mL bottles is 501.2 mL.A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

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?

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?

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.From your sample of 15 gas stations,you calculate a 95% confidence interval of ($1.34,$1.40)

A random sample of 30 long distance runners aged 20-25 was selected from a running club.The resting heart rates (in beats per minute)of the runners are shown below.Estimate the mean resting heart rate for the population of long distance runners aged 20-25.Give the 95% confidence interval.

99% confidence interval with df = 24