Exam 11: Two-Sample Tests of Hypothesis

When sample sizes are less than 30,a test for the differences between two population means has n-1 degrees of freedom.

When can a paired-t test be used to test a hypothesis of no difference between population means?

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the variances are pooled to compute the best estimated variance.

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings.It is important that the diameters be as close as possible to an industry standard.The output from each process is sampled and the average error from the industry standard is calculated.The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors.Assume that the population standard deviations are equal. What is the degrees of freedom?

Two samples,one of size 14 and the second of size 13,are selected to test the difference between two population means.How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings.It is important that the diameters be as close as possible to an industry standard.The output from each process is sampled and the average error from the industry standard is calculated.The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors.Assume that the population standard deviations are equal. If the calculated value of t is +2.70,what would be the decision using the 0.01 level of significance?

A statistics professor wants to compare grades in two different classes of the same course.This is an example of a paired sample.

Of 250 adults who tried a new multi-grain cereal,"Wow!",187 rated it excellent;of 100 children sampled,66 rated it excellent.Using the 0.1 significance level and the alternate hypothesis not equal to ,what is the null hypothesis?

A study by a bank compared the average savings of customers who were depositors for three years or less,with those who had been depositors for more than three years.The results of a sample are: If $\alpha$ = .05 and the p-value is 0.146,what is the decision rule regarding the null hypothesis?

When dependent samples are used to test for differences in the means,we pool the sample variances.

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

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 (n₁ + n₂ - 2)degrees of freedom.

If we are testing for the difference between two population proportions,it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

In a market test of a new chocolate raspberry coffee,a poll of 400 people (sample 1)from Dobbs Ferry showed 250 preferred the new coffee.In Irvington,170 (sample 2)out of 350 people preferred the new coffee.To test the hypothesis that a higher proportion of people in Dobbs Ferry prefer the new coffee,what is the alternate hypothesis?

When independent samples are used to test for differences in the means,we pool the sample variances.

When testing for a difference between the means of two dependent samples,n₁ = n₂.

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

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 your decision if $\alpha$ = 0.01 and the z-statistic is -1.96? ____________________

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

The pooled estimate of the proportion is found by dividing the total number of successes by the total number of observations.