Exam 11: Two-Sample Tests of Hypothesis

For hypotheses that compare two population means, what test statistic is used when the population standard deviations are known?

Of 250 adults who tried a new multi-grain cereal, "Wow!", 187 rated it excellent; of 100 children sampled, 66 rated it excellent. What is the pooled proportion?

When testing the hypothesized difference between two population means, the implied hypothesis is

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, then the test has _________ degrees of freedom.

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region?

A company is researching the effectiveness of a new web site design to decrease the time to access a website. Five web site users were randomly selected and their times (in seconds) to access the web site with the old and new designs were recorded. The results follow. What is the value of the test statistic?

A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds? What decision is made about the null hypothesis using and a = 0.05? ____________

The paired t test is especially appropriate when the sample sizes of two groups are _______.

If two independent samples of sizes 20 and 10 with equal standard deviations are used to test the difference between the means, the degrees of freedom for a t-statistic are _____.

When independent samples, with unknown, unequal standard deviations, are used to test for differences in the means, we pool the sample variances.

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the alternate hypothesis?

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? What is the alternate hypothesis? _______________________

Assuming the population variances are known, the population variance of the difference between two sample means is

In testing the difference between two population proportions, we pool the two sample proportions to estimate the population proportion.

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? Using the 1% level of significance, what is the critical value? _____

If we are testing for the difference between two population proportions, it is assumed that the sample observations from one population are _____________ of the sample observations from the other population.

When dependent samples are used to test for differences in the means, we compute ________________ differences.

If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Using two independent samples, we test for a hypothesized difference between two population means. The population standard deviations are unknown but assumed equal. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value?

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the critical value?