Question

Joan moves into her new apartment and wants to purchase a new couch. She wants to determine if the average cost of couches at Store 1 is cheaper than Store 2. At Store 1 the average cost of 20 couches is $650 with a standard deviation of $61. At Store 2 the average cost of 22 couches is $730 with a standard deviation of $78. At alpha = .05, what are the results if you want to determine that Store 1 is cheaper than Store 2 in couch prices? Accept H0, the test statistic is greater than -2.021. Reject H0 the test statistic is less than -2.021. Accept H0 the test statistic is greater than -1.684. Reject H0 the test statistic is less than -1.684.

Answer 1

The answer is:

Reject H0 the test statistic is less than -1.684.

Explanation:

The provided sample means are shown below:

Also, the provided sample standard deviations are:

and the sample sizes are

.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha:

This corresponds to a left-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=40. In fact, the degrees of freedom are computed assuming that the population variances are equal.

Hence, it is found that the critical value for this left-tailed test is tc​=−1.684, for α=0.05 and df=40.

The rejection region for this left-tailed test is R={t:t<−1.684}

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