Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

If the researcher computes the probability of the calculated statistic and compares it to alpha, the level of significance to reach a decision, the researcher is using the p-value method for testing the hypotheses.

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

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 ___.

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 null hypothesis 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.Fifty-four of the messages were not business related.The null hypothesis 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 decision rule for this problem is to reject the null hypothesis if the observed "t" value 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 ___.

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

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

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

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 ___.

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 ___.

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 ___.

Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60.The sample size is 64 and $\alpha$ = .05.If the sample mean is 58 and the population standard deviation is 16, the observed z value is ___.

A company produces an item that is supposed to have a six centimetre hole punched in the centre.A quality control inspector is concerned that the machine which punches the hole is "out-of-control" (hole is too large or too small).In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole.The alternative hypothesis used to statistical test to determine if the machine is out-of-control is

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

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 appropriate decision is ___.

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 null hypothesis 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.Fifty-four of the messages were not business related.The appropriate decision is __.

Whenever hypotheses are established such that the alternative hypothesis is "not equal to", the hypothesis test would be a two-tailed test.