Question

Choose the data set from at least one of your classmates. Use a 0.05 significance level to test the claim that was made about the average high temperature using the data set provided by this classmate. Note that we will treat this data set as a random sample, representing all June days in the community. Show all steps, including your hypotheses, your critical values, your test statistic and your conclusion. Post a picture of your work. Was your classmate's guess correct? Explain.

Null hypothesis 85° F

94 91 95 93 78 88 90 90 91 90 81 87 88 89 90 90 86 90 91 92 93 92 92 83 80 89 92 93 81 87

88.86666667 Mean

4.344900565 Standard Deviation

Answer 1

(STEP 1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 85

Ha: μ ≠ 85

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(STEP 2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is tc​=2.045.

The rejection region for this two-tailed test is R={t:∣t∣>2.045}

(STEP3) Test Statistics

The t-statistic is computed as follows:

(STEP 4) Decision about the null hypothesis

Since it is observed that ∣t∣=4.884>tc​=2.045, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.000, and since p=0.000<0.05, it is concluded that the null hypothesis is rejected.

(STEP5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 85 F, at the 0.05 significance level.