Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

The weight of a USB flash drive is 30 grams and is normally distributed. Periodically,quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise,the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams,respectively.The null hypothesis is ______.

Hypotheses are tentative explanations of a principle operating in nature.

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. Sixty of the messages were not business related. The appropriate decision 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 observed value of chi-square is ________.

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.

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 appropriate decision is:

Consider the following null and alternative hypotheses. These hypotheses ______________.

Generally speaking,the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

A statistically significant result is _______________.

Suppose a researcher is testing a null hypothesis that $\mu$ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed t value is _______.

In testing hypotheses,the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

The executives of CareFree Insurance,Inc.feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is __________.

The value of committing a Type II error is defined by the researcher prior to the study.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 and a two?tailed test is +1.96.The observed z value from sample data is 2.85.The decision made by the researcher based on this information is to _____ the null hypothesis.

The executives of CareFree Insurance,Inc.feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________.

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 and 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 rejection and nonrejection regions are divided by a point called the critical value.

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

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. Ophelia's null hypothesis is _______.

In a two-tailed hypothesis about a population mean with a sample size of 100, $\alpha$ is known,and α = 0.05,the rejection region would be _______.