10.2 Two Population Means with Known Standard Deviations
The rarer case where population spreads are already given, so the difference of sample means is exactly normal and the statistic is a z rather than a t.
Introductory Statistics 2e, 10.2 Two Population Means with Known Standard Deviations
11 exercises
10.2 Exercise 4
The average age of 10 professors selected randomly in university A is 46.672 with a standard deviation of 8.53. The average age of 10 professors selected randomly in university B is 47.531 with a standard deviation of 7.83.
Does the data indicate that university A has older professors than university B, on average? Test at a 5% level of significance.
10.2 Exercise 5
What is the random variable?
10.2 Exercise 7
What is the test statistic?
10.2 Exercise 9
At the 1% significance level, what is your conclusion?
10.2 Exercise 11
State the null and alternative hypotheses.
10.2 Exercise 15
State the null and alternative hypotheses.
10.2 Exercise 17
What is the p-value?
10.2 Exercise 19
At the 1% significance level, what is your conclusion?
10.2 Exercise 21
Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not…
10.2 Exercise 23
Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectivel…
10.2 Exercise 25
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement “I’m pleased with the way we divide the responsibilities for childcare.” The ratings went from one (strongly agree) to five (strongly disagree). the table contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband’s versus…
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.