The following hypotheses were tested: H_0: mu = 75 versus H_a: mu > 75 where I1/

Question

The following hypotheses were tested: H_0: mu = 75 versus H_a: mu > 75 where I1/4 is the true mean score for MD4 Epi finals. The test scores of a random sample of students who have taken MD4 Epi had a mean x-bar = 78. The hypothesis test produced a P-value of 0.0314. With alpha = 0.05, do the data give sufficient evidence that the mean final score is greater than 75? A. No, because the p-value is not less than alpha B. No, because the results are statistical significant. C. No, because the p-value is less than alpha D. Yes, because the p-value is not less than alpha. E. Yes, because the p-value is less than alpha.

Explanation / Answer

Solution:-

The P-value is the probability of observing a sample statistic as extreme as the test statistic.

A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level, and is often denoted by .

Since the P-value (0.0314) is less than the significance level (0.05), we cannot accept the null hypothesis.

Thus, we accept the alternate hypothesis that Ha > 75.

Option E is correct, that the data give significant evidence that the mean final score is greater than 75, because the p-value is less than alpha.

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