Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.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 null hypothesis is ________.

If a null hypothesis was not rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results.

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

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the test would be _______.

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.The sample size is 25 and α =.05.If the sample mean is 50 and the population standard deviation is 8, the observed z value is _______.

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 _______.

In performing hypothesis tests about the population mean, if the population standard deviation is not known, a t test can be used to test the mean if _________________.

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces.If the sample variance of the dispensed liquid delivered per cup is 0.81 ounces, and α = 0.05, the appropriate decision is to ________.

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls, for which you obtain an average waiting time of 8.15 minutes.Suppose that you can assume that waiting times are normally distributed.The sample standard deviation is 4.2 minutes.The null hypothesis is:

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

The probability of committing a Type I error is called the power of the test.

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

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes.If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the p-value is approximately

A car manufacturer looks at past sales and realizes that the most common car color is silver with 24% of purchasers selecting that color.The dealerships in one state believe that car purchasers in their area believe that the proportion of purchasers selecting silver is greater than 24%.Based on a survey of 84 car purchasers in the state, the dealerships find that 26% of them would select silver.If the true proportion selecting silver is 27%, what is the power, given an alpha of 0.05?

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs at minimum number of swimmers to sign up in order to be cost effective.Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15.Suppose the instructor wants to conduct a hypothesis test.The alternative hypothesis for this hypothesis test is: "the population mean is less than 15".The sample size is 8, $\sigma$ is known, and α =.05, the critical value of z is _______.

Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8", where μ is the population mean, the hypothesis test would be a two-tailed test.

Consider the following null and alternative hypotheses. H_o: $\mu$ $\le$ 67 H_a: $\mu$ > 67 These hypotheses _______________.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a one-tailed test is 1.645.The observed z value from sample data is 1.13.The decision made by the researcher based on this information is to ______ the null hypothesis.

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.