Exam 20: Inferences About Means

A sociologist develops a test to measure attitudes about public transportation.She wishes to compute a 90% 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?

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

A credit union took a random sample of 40 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2193 < μ(balance)< $3828.

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

The owner of a football team claims that the average attendance at games is over 74,100,and he is therefore justified in moving the team to a city with a larger stadium.An independent investigator will conduct a hypothesis test to determine whether his claim is accurate.

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.

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. 62 70 61 64 75 54 72 68 74 54 75 70 62 66 79 73 81 60 66 76 67 62 66 69 70 86 76 60 53 71

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?

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?

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

95% confidence interval with df = 15

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.

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?

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)

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

A 90% confidence interval from a sample of size 20

Consider a right skewed distribution.What is the shape of the sampling distribution for the sample mean based on samples of 50 observations?

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?

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline with 90% confidence.You believe that the standard deviation of prices is $0.04.If you wish to achieve a margin of error no larger than $0.02,how many gas stations should you sample?

The amounts (in millilitres)of juice in eight randomly selected juice bottles are: 443.55 467.21 443.55 449.46 470.16 464.25 443.55 467.21 Construct a 98% confidence interval for the mean amount of juice in all such bottles.