Question Help 8.4.17 For the following claim, find the null and alternative hypo

Question

Question Help 8.4.17 For the following claim, find the null and alternative hypotheses est statistic, critical value, and draw a conclusion. Assume that a simple random sample has been selected from a normally distributed population. Answer parts a-d. Claim: The mean IQ score of statistics professors is greater than 124. Sample data: n 8, x 27, s-4. The significance level is o -0.05. Click the icon to view a table of critical values a. Choose the correct null hypothesis (Ho) and alternative hypothesis (H1) O A. Ho: u 124 H 1: 124 O B. Ho: H 124 H1:

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 124
Alternative hypothesis: > 124

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.+

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n) = 4 / sqrt(18) = 0.94280904158
DF = n - 1 = 18 - 1 = 17
t = (x - ) / SE = (127 - 124)/0.94280904158 = 3.18198051535 or 3.182

Where critical t value from the table is 2.110.therfore the corresponding P-Value is 0.024991.

Here is the logic of the analysis: Given the alternative hypothesis ( > 124), we want to know whether the observed sample mean is large enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of 3.182. We use the t Distribution Calculator to find P(t < 3.182)

The P-Value is 0.002727.
The result is significant at p < 0.05

Interpret results. Since the P-value (0.002727) is smaller than the significance level (0.05), we can reject the null hypothesis.

Conclusion. Reject the null hypothesis. Thus, we have sufficient eveidence to prove the claim that the mean IQ score of statistics professors is greater than 124.

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