Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

David Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.Based on a recent census of personnel,David knows that the variance of worker training time in New Brunswick is 8,and he wonders if the variance in Nova Scotia is the same number.His staff randomly selected personnel files for 15 workers in Nova Scotia,and determined that their mean training time was 25 hours and that the standard deviation was 4 hours.Assume that worker training time is normally distributed in the population.Using $\alpha$ = 0.10,the observed value of chi-square is ___.

A null hypothesis is p > 0.65.To test this hypothesis,a sample of 400 is taken and alpha is set at 0.05.If the true proportion is p = 0.60,what is the probability of a Type II error?

David Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.Based on a recent census of personnel,David knows that the variance of worker training time in New Brunswick is 8,and he wonders if the variance in Nova Scotia is the same number.His staff randomly selected personnel files for 15 workers in Nova Scotia,and determined that their mean training time was 25 hours and that the standard deviation was 4 hours.Assume that worker training time is normally distributed in the population.Using $\alpha$ = 0.10,the critical values of chi-square are ___.

The diameter of 3.5 centimetre discs is normally distributed.Periodically,quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment;otherwise,the punching process continues.The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres,respectively.Using $\alpha$ = 0.05,the critical "t" values are ___.

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 ___.

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.

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 ___.

Consider the following null and alternative hypotheses: H_o: p $\le$ 0.16 H_a: p > 0.16 These hypotheses ___.

In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10,the rejection region would be ___.

Reach a statistical conclusion in hypothesis testing problems about a population proportion using the z statistic.

Elwin Osbourne,CIO at GFS,Inc. ,suspects that at least 25% of email messages sent by GFS employees are not business related.A random sample of 300 email 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 ____.

Reach a statistical conclusion in hypothesis testing problems about a population variance using the chi-square statistic.

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

Whenever hypotheses are established such that the alternative hypothesis is ">",then this would be a two-tailed test.

Solve for possible Type II errors when failing to reject the null hypothesis.

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 appropriate decision is ___.

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

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 degrees of freedom associated with this are ___.

Ophelia O'Brien,VP of Consumer Credit of Credit First Banks (CFB),monitors the default rate on personal loans at the CFB 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 ___.

Consider the following null and alternative hypotheses: H_o: p $\ge$ 0.16 H_a: p < 0.16 These hypotheses ___.