Exam 9: Hypothesis Testing

One-tailed alternative hypotheses are phrased in terms of:

Of type I and type II error, which is traditionally regarded as more serious?

A chi-square goodness-of-fit test can be used to test for normality.

A marketing research consultant hired by Red Bull^® is interested in determining if the proportion of customers who prefer Red Bull^® to other energy drink brands is over 50%. A random sample of 200 consumers was selected from the market under investigation, 55% favored Red Bull^® over other brands. Additional information is presented below. -(A) If you were to conduct a hypothesis test to determine if greater than 50% of customers prefer Red Bull^® to other brands, would you conduct a one-tail or a two-tail hypothesis test? Explain your answer. ​ (B) How many customers out of the 200 sampled must have favored Red Bull^® in this case? ​ (C) Using a 5% significance level, can the marketing consultant conclude that the proportion of customers who prefer Red Bull^® exceeds 50%? Explain your answer. ​ (D) If you were to use a 1% significance level, would the conclusion from (C) change? Explain your answer.

The test statistic employed to test is , which is F distributed with degrees of freedom.

The alternative hypothesis is also known as the:

A null hypothesis can only be rejected at the 10% significance level if and only if:

Tests in which samples are not independent are referred to as matched pairs or paired samples.

The retailing manager of Meijer supermarket chain in Michigan wants to determine whether product location has any effect on the sale of children toys. Two different aisle locations are considered: front and rear. A random sample of 18 stores is selected, with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all the stores. At the end of one-month trial period, the sales volumes (in thousands of dollars) of the product in each store are as shown below: -At the 0.05 level of significance, is there evidence of a significant difference in average sales among the various aisle locations?

The p-value of a test is the smallest level of significance at which the null hypothesis can be rejected.

Which of the following statements is true regarding the chi-square goodness-of-fit test for normality?

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

A test with a 0.10 significance level has a larger rejection region than a test with a 0.05 significance level.

A low p-value provides evidence for accepting the null hypothesis and rejecting the alternative.

The form of the alternative hypothesis can be:

In conducting hypothesis testing for difference between two means when samples are dependent (paired samples), the variable under consideration is ; the sample mean difference between the pairs.

A null hypothesis can only be rejected at the 5% significance level if and only if:

An example of a paired sample is the number of defective computer chips of a particular type from two different manufacturers.

If, instead, the test is conducted at the 0.10 significance level, would the decision regarding the salaries change? Explain why or why not. Answer this question without re-running the hypothesis test. ​

Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. -(A) Can the sample size be determined from the information above? Yes or no? If yes, what is the sample size in this case? (B) The firm believes that the mean life is actually greater than 1500 hours, should you conduct a one-tailed or a two-tailed hypothesis test? Explain your answer, and state the appropriate null and alternative hypotheses. (C) What is the sample mean of this data? If you use a 5% significance level, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer. (D) If you were to use a 1% significance level in this case, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.