7. Question 9.112 A random sample of size 1000 has x-104. The significance level

Question

7. Question 9.112 A random sample of size 1000 has x-104. The significance level ? is set at 0.05. The p- value for testing Ho: ? 100 against Ha: ?#100 is 0.057. Explain what is incorrect about each of the following interpretations of this p-value and provide a proper interpretation. a. The probability that the null hypothesis is correct equals 0.057. b. The probability that 104 if Ho is true equals 0.057 c. If in fact ?#100 so Ho is false, the probability equals 0.057 that the data would show at least as much evidence against Ho as the observed value. d. The probability of a Type I error equals 0.057 e, we can accept Ho at the ?-0.05 level f. we can reject Ho at the ?-0.05 level

Explanation / Answer

Ans:

The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true – the definition of 'extreme' depends on how the hypothesis is being tested.

When p-value>alpha,we fail to reject the null hypothesis.

When p-value<=alpha,we reject the null hypothesis.

Given that

p-value=0.057

As,p-value>0.05,we can accept the null hypothesis.

Only option e is correct.

Type I error=alpha=0.05(So,option d is incorrect)

a,b,c are incorrect,as p-value definition is incorrect.

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