Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

A home building company routinely orders standard interior doors with a height of 80 inches.Recently the installers have complained that the doors are not the standard height.The quality control inspector for the home building company is concerned that the manufacturer is supplying doors that are not 80 inches in height.In an effort to test this,the inspector is going to gather a sample of the recently received doors and measure the height.The alternative hypothesis for the statistical test to determine if the doors are not 80 inches is

The lifetime of a squirrel follows a normal distribution with mean μ = 40 months and a standard deviation $\sigma$ = 7 months.To test the hypothesis that μ > 40,25 squirrels are randomly selected.Assuming that μ = 45,and α = 0.1,the probability of type II error is approximately

A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation $\sigma$ = 6 months.To test the alternative hypothesis that μ < 22 with α = .01,36 laptop batteries are randomly selected.Assuming that μ = 24,the probability of type II error is approximately

In testing a hypothesis about a population variance,the chi-square test is fairly robust to the assumption the population is normally distributed.

Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60,against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and $\alpha$ = .05. If the sample mean is 58 and the population standard deviation is 16,the observed z value is _______.

The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.

A small restaurant owner believes at least 36 % of his customers would be willing to order take out service if it were available.He is interested in surveying his customer base.He intends to use the following null and alternative hypotheses. These hypotheses _______________.

In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23,a random sample of 17 items is selected. The sample mean is 24.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state.She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate.The observed z value for this problem is _______.

When conducting a hypothesis test on a population proportion,the value of q is defined as p + 1.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using $\alpha$ = 0.10,the observed z value is _______.

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46,against the alternative hypothesis that the population mean is greater than 46.If the sample size is 25, $\sigma$ is known,and α = .01,the critical value of z is _______.

A "scientific hypothesis" _______________.

If a null hypothesis is not rejected at the 0.05 level of significance,the p-value is bigger than 0.05

Jennifer Cantu,VP of Customer Services at Tri-State Auto Insurance,Inc.,monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week,her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's null hypothesis is ________.

Elwin Osbourne,CIO at GFS,Inc.,suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The null hypothesis is ____.

David Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks. Based on a recent census of personnel,David knows that the variance of teller training time in the Southeast region is 8,and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region,and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using $\alpha$ = 0.10,the appropriate decision is ________.

Elwin Osbourne,CIO at GFS,Inc.,suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is _______.

When a false null hypothesis is rejected,the researcher has made a Type II error.

In a two-tailed hypothesis about a population mean with a sample size of 100, $\alpha$ is known,and α = 0.10,the rejection region would be _______.