I know that the answer to 18 is C, but I am having some trouble with the next tw

Question

I know that the answer to 18 is C, but I am having some trouble with the next two questions

18 You work for a charitable organization and you want to estimate the average age of the people who donate to your organization. You get a random sample of n 120 donors and the value of the sample mean is 42 years. The value of the sample standard deviation is 19 years. The lower and upper end of the 95% confidence interval for the average age of people who donate to your organization are: a [36.4, 47.6 b 137.5, 46.5] c 38.6, 45.4] d 139.8, 44.2] 19 In the previous question you want to test the hypothesis, at the 5 percent level of significance, that the average age is at least 45 years. Compute the probability value for the test. 0.042 Reject the null hypothesis and conclude the mean age is less than 45 0.042 Do not reject the null hypothesis. Conclude the mean age is not less than 45 0.004 Reject the null hypothesis and conclude the mean age is less than 45 0.004 Do not reject the null hypothesis. Conclude the mean age is not less than 45 20 Regardless how you answered the previous question, which of the following statements is correct? a If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type II error. b If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type I error. c If the mean age is less than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type I error d If the mean age is in at least than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type II error

Explanation / Answer

For the above questions output is genertaed by using Minitab software :

One sample t test is used to test the hypothesis :

Question 18 :

One-Sample T

N Mean StDev SE Mean 95% CI
120 42.0000 19.0000 1.7345 (38.5656, 45.4344)

Question 19 :

One-Sample T

Test of mu = 45 vs mu < 45

i.e H0 =mean age is equal to 45 years

vs H1= mean age is less than 45 years

95%
Upper
N Mean StDev SE Mean Bound T P
120 42.0000 19.0000 1.7345 44.8753 -1.73 0.042

As p value =0.042 < alpha =0.05 we fail to accept H0 and conclude the mean age is less than 45 years.

Question 20 :

Type I error is Rejecting H0 when it is true

Type II error is Accepting H0 when it is false

So here option (A) will be correct i.e If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type II error.

beacuse You commit a Typt II error when you do not reject a false null hypothesis.

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