Exam 11: Hypothesis Testing for Single Populations

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

Consider the following null and alternative hypotheses: H₀: π $\ge$ 0.16 H_a: π < 0.16 These hypotheses ___.

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

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 ___.

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

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 ___.

Which of the following is not one of the eights steps in the hypothesis testing procedure?

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

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

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

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and an one?tailed test is 1.645. The test statistic from sample data is 1.13. The decision made by the researcher based on this information is to ___ the null hypothesis.

If the chosen significant level is 5%, then there is a

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 test statistic for this problem is ___.

A university wants to increase its retention rate of 4% for graduating students from the previous year. The null and alternative hypotheses to test if retention rate did increase will be?

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ 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 $\textbf{ not }$ business related. The appropriate decision 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 3.55 and 0.08 centimetres, respectively. Using $\alpha$ = 0.05, the appropriate decision is ___.

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.

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

When a researcher fails to reject a $\textbf{ false }$ null hypothesis, a Type II error has been committed.

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 ___.