Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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. These hypotheses _______________.

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 16 cups of the dispensed liquid with sample mean of 7.75 ounces and sample variance of 0.81 ounces. If the dispensed liquid delivered per cup is normally distributed,the appropriate decision at α = 0.05 is

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 -2.11.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. Ninety employees rate the management as participatory. The appropriate decision is __________.

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 _________________.

Suppose that The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption.You need to decide if you will use water coming from a specific source for one of the beverages your company produces,based on sample measures of this pollutant taken in random different locations and times at the source of water.In this case you would want to

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 ?1.85.The decision made by the researcher based on this information is to _____ the null hypothesis.

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8",where μ is the population mean,the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

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 _______.

Power is equal to (1 - $\beta$ ),the probability of a test rejecting the null hypothesis that is indeed false.

A small restaurant owner believes no more than 36% of his customers travel over 10 miles to his business.He is interested in expanding his customer base through marketing.However,he would like to test his hypothesis prior to investing money in a marketing initiative.He intends to use the following null and alternative hypotheses. These hypotheses _______________.

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

Discrete Components,Inc.manufactures a line of electrical resistors. Presently,the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically,the quality control inspectors check for conformity by randomly select 10 resistors from the line,and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using $\alpha$ = 0.05,the observed value of chi-square is _________________.

In conducting the z test of proportions,the sample proportion is computed by dividing the number of items being counted by the estimated total population.

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

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 critical values of chi-square are ________.

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 null hypothesis is ________.

The p-value is

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.