Exam 20: Inferences About Means

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 scientist in Smallville tested the cholesterol of a random sample of 35 town residents.He constructed the following confidence interval: t-interval for μ: with 99.00% Confidence, 188 < μ(Cholesterol)< 206

A test of sobriety involves measuring the subject's motor skills.Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.4.At a significance level of 0.01,test the claim that the true mean score for all sober subjects is equal to 39.0.

P-value for a left tailed test with a test-statistic of -1.15 from a sample of size 21.

P-value for t ≤ 2.13 for a sample of size 31

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?

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.

Suzie has installed a new spam blocker program on her email.She used to receive an average of 20 spam emails a day.Is the new program working?

P-value for a two tailed test with a test-statistic of 1.55 from a sample of size 29.

You are considering moving to Richmond Hill,and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 50 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

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 95% confidence interval with df = 29

99% confidence interval with df = 24

Suppose that scores for men on an aptitude test have greater variability than scores for women on the same test.In other words,the population standard deviation is greater for the population of men than for the population of women.Based on a sample of size 50,a 95% confidence interval for the mean score,μ,of all women has a margin of error of 2.2.Which of the following confidence intervals will have a smaller margin of error? I.A 99% confidence interval for the mean score of women.Sample size = 50 II.A 95% confidence interval for the mean score of women.Sample size = 100 III.A 95% confidence interval for the mean score of men.Sample size = 50

Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from $119.1 \mathrm {~cm}$ to $125.9 \mathrm {~cm}$ .

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.

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 34 randomly selected juice bottles are measured.Of the 34 bottles,21 contained less than 473 mL,4 contained exactly 473 mL,and 9 contained more 473 mL.Perform a sign test to determine if the median amount is less than 473 mL.Use a 5% level of significance.

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $\$ 1200 .$ They suspect that the average fee charged by one particular clinic for this procedure is higher than $\$ 1200 .$ The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

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.

P-value for a right tailed test with a test-statistic of 1.55 from a sample of size 29.