Exam 9: Statistical Inference: Hypothesis Testing for Single Populations

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 ___.

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 ___.

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 ___.

In a two-tailed hypothesis about a population mean with a sample size of 100 and α = 0.05, the rejection region would be ___.

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.If the sample size is 49 and alpha = .10, the critical value of z 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 ___.

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 ___.

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

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 test would be ___.

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?

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 alternative hypothesis would be ___.

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

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 ___.