A truetalse test has 40 questions. Suppose a passing grade is 26 or more correct

Question

A truetalse test has 40 questions. Suppose a passing grade is 26 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 26 answers correct out of 40. Use a significance level of 0.05. Stepe 1 and 2 of a hypothesis test procedure are given below. Show step 3, finding the test statistic and the p-value and step 4, interpreting the results. runch ice Proble e Quizzes ebook Step 1: Ho p-0.50 H p 0.50 the sample is random Step 3 Compute the z-test statistic, and the p-value ter Conter for Suo media Libirl z" (Round to two decimal places as needed) pvalue " (Round to three decimal places as needed.) Step 4 Do you reject or not reject the null hypothesis? What doos this mean in the context of the data? A. Rejed H0 The probablity or doing this well by chance alone is not small enough to conclude that the student is not guessing. Click to select your answer(s). Sample Tests and Quizzes

Explanation / Answer

p = 26/40 = 0.65

Standard deviation = sqrt ( P (1 - P)/n)

= sqrt(0.5 * 0.5/40) = 0.08

Z = (p - P)/SD

= (0.65 - 0.5)/0.08 = 1.88

P-VALUE = P(Z > 1.88)

= 1 - P(Z < 1.875)

= 1 - 0.9699 = 0.03

As the p-value is less than the alpha value 0.05 SO the null hypothesis is rejected.

Option-C is the correct answer.

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