Exam 13: Inference About Comparing Two Populations

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means .Assume the population variances are known.The sampling distribution of the sample mean difference is:

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal, two independent samples are drawn from the populations.Which of the following tests is appropriate?

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

In testing the difference between the means of two normal populations using two independent samples when the population variances are unequal, the sampling distribution of the resulting statistic is:

In testing the hypothesis vs. , two random samples from two normal populations produced the following statistics: .What conclusion can we draw at the 1% significance level?

When testing for the difference between two population variances with sample sizes of n₁ = 8 and n₂ = 10, the degrees of freedom are:

The expected value of the difference between two sample proportions is the ____________________ of/between their corresponding population proportions.

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by ____________________.

The service manager of a car dealer wants to determine if owners of new cars (two years old or less) tune up their cars more frequently than owners of older cars (more than two years old).From his records he takes a random sample of ten new cars and ten older cars and determines the number of times the cars were tuned up in the last 12 months.The data follow.Do these data allow the service station owner to infer at the 10% significance level that new car owners tune up their cars more frequently than older car owners?

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations, we:

Random samples from two normal populations produced the following statistics: , , , and .Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?

Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. -{Senatorial Election Narrative} What is the p-value of the test?

A matched pairs experiment decreases variability (compared to two independent samples).

When the population variances are unequal, we estimate each population variance with its sample variance.Hence, the unequal-variances test statistic of is approximately Student t-distributed with n₁ + n₂ -2 degrees of freedom.

The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n₁ and n₂ are large.

A Marine boot camp instructor recorded the time in which each of 15 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred, the instructor would use a t-distribution with 15 degrees of freedom.

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as:

The t-test for the difference between the means of two independent populations assumes that the respective:

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.

Pooling is made possible by hypothesizing (under the null hypothesis) that p₁ __________ p₂.