Question

Practice Computing Hypothesis Test with a Computer In this worksheet we are going to focus on hypothesis test with the aid of a computer.Provided below are the basic steps of calculating a hypothesis test. You want to start by determining whether you are interested in working with a mean or a proportion. Then identify each of the parts listed below In order to use the formulas for a hypothesis test we first need to confirm that the sample size requirements for the central limit theorem are satisfied. See the notes for more information. If the sample size is not met acknowledge that you need to proceed with caution. Identify the null and alternative hypotheses. The null hypothesis will be listed first. Calculate the appropriate test statistic. When working with proportions you will calculate a z- statistic. When working with means you will calculate a t-statistic. Compare your test statistic to the appropriate distribution to find the p-value. Conclude the test in context of the problem 1. 2. 3. 4. 5. For each of the four problems below use the online applications in the notes to calculate the hypothesis test. In your response provide all of the steps listed above. For the test statistic and p-value you do not need to show your work you only need to give the values provided by the applications 1. A study was conducted to see if there was a difference in how men and women feel about animal testing. A random sample of 55 women was selected and asked to rank how they felt about animal testing on a 10 point scale where a score of 1 represented strong opposition and a score of 10 represented strong support. The mean score of the sample was 4.5 with a standard deviation of 0.7. A random sample of 75 men was selected and asked to rank how they felt about animal testing on a 10 point scale where a score of 1 represented strong opposition and a score of 10 represented strong support. The mean score of the sample was 5.2 with a standard deviation of 0.9. Test the claim that there is a difference in how men and women feel about animal testing. Use a-0.01. 2. EKU would like to know if fewer seniors pan on staying in Kentucky after graduation compared to freshman. A random sample of 100 seniors are surveys and 71 responded that they plan on staying in Kentucky after graduation. A random sample of 100 freshman are surveys and 82 responded that they plan on staying in Kentucky after graduation. Use α-0.05.

Answer 1

Solution to 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: $\mu_1 = \mu_2$

Ha: $\mu_1 \ne \mu_2$

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

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the degrees of freedom are df=128. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=2.615, for α=0.01 and df=128.

The rejection region for this two-tailed test is R={t:∣t∣>2.615}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=4.799>tc​=2.615, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is different than μ2​, at the 0.01 significance level.

Confidence Interval

The 99% confidence interval is 1.081<μ1​−μ2​<−0.319.

Graphically

$normaldistributiongrapher.php?mean=0&sig$

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