Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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 ___.

When a true null hypothesis is rejected,the researcher has made a Type I error.

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 ___.

Consider the following null and alternative hypotheses. H_o: µ = 67 H_a: µ $\neq$ 67 These hypotheses ___.

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9,a random sample of 16 items is selected.The sample mean is 7.1 and the sample standard deviation is 2.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is ___.

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9,a random sample of 16 items is selected.The sample mean is 7.1 and the sample standard deviation is 2.4.It can be assumed that the population is normally distributed.The level of significance is selected as 0.05.The table "t" value for this problem is ___.

Hypotheses are tentative explanations of a principle operating in nature.

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

The rejection and nonrejection regions are divided by a point called the critical value.

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 null hypothesis is ___.

Suppose the alternative hypothesis in a hypothesis test is: "the population mean is less than 60".If the sample size is 50 and alpha =.05,the critical value of z is ___.

Suppose you are testing the null hypothesis that a population mean is less than or equal to 80,against the alternative hypothesis that the population mean is greater than 80.The sample size is 49 and alpha =.05.If the sample mean is 84 and the population standard deviation is 14,the observed z value is ___.

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 critical value of chi-square is ___.

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 ___.

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.Sixty of the messages were not business related.The appropriate decision is ___.

Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60".If the sample size is 80 and alpha = .01,the critical value of z is ___.

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

Reach a statistical conclusion in hypothesis testing problems about a population mean with an unknown population standard deviation using the t statistic.

When a researcher fails to reject a false null hypothesis,a Type II error has been committed.

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