Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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 ___.

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 appropriate decision is ___.

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 38 defaulted loans.Using $\alpha$ = 0.10,the appropriate decision is ___.

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.Using $\alpha$ = 0.10,the observed z value is ___.

Jennifer Cantu,VP of Customer Services at Tri-City Auto Insurance Inc. ,monitors the claims processing time of the claims division.Her standard includes "a mean processing time of 5 days or less." Each week,her staff checks for compliance by analyzing a random sample of 60 claims.Jennifer's null hypothesis is ___.

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

The probability of committing a Type I error is called the power of the test.

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 ___.

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief,a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchased this company's brand of the product.If a researcher wants to conduct a statistical test for this problem,the observed z value would be ___.

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 ___.

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 ___.

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 level of significance is selected to be 0.10.The table "t" value for this problem is ___.

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

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

In performing hypothesis tests about the population mean,the population standard deviation should be used if it is known.If it is not known,which of the following statistical test should be used?

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 ___.

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.Using $\alpha$ = 0.10,the appropriate decision 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

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.Using $\alpha$ = 0.10,the critical z value is ___.

Develop both one- and two-tailed null and alternative hypotheses that can be tested in a business setting by examining the rejection and nonrejection regions in light of Type I and Type II errors.