Step 1 :The problem is asking for the test statistic and p-value for a sample of 74 stocks, where 28 went up. This is a hypothesis testing problem for a proportion. The null hypothesis is that the proportion of stocks that went up is 0.3, and the alternative hypothesis is that the proportion is more than 0.3.
Step 2 :To calculate the test statistic, we need to use the formula for the z-score in hypothesis testing for a proportion, which is \((p_{hat} - p_0) / \sqrt{(p_0 * (1 - p_0)) / n}\), where \(p_{hat}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and n is the sample size.
Step 3 :Given that n = 74, x = 28, \(p_0\) = 0.3, and \(\alpha\) = 0.05, we can calculate \(p_{hat}\) as 0.3783783783783784.
Step 4 :Substituting these values into the formula, we get a z-score of approximately 1.471.
Step 5 :To calculate the p-value, we need to find the probability of getting a z-score as extreme as the one we calculated, under the null hypothesis. This is done by finding the area under the standard normal curve to the right of the calculated z-score.
Step 6 :The calculated p-value is approximately 0.071.
Step 7 :The p-value is greater than the significance level of 0.05, which means we do not reject the null hypothesis that the proportion of stocks that went up is 0.3.
Step 8 :Final Answer: The test statistic for this sample is approximately \(\boxed{1.471}\). The p-value for this sample is approximately \(\boxed{0.071}\).