Question

The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498. To perform this study we should form a null hypothesis stating that the average is .__________(A. less than. B. less than or equal to. C. equal to. D. greater than. E. greater than or equal to).

At the 10% significant level, the p-value/statistics is ________ (keep to 3 decimal points), so we should ____________ (A. Reject. B. Not reject) the null hypothesis.

Hence, we may conclude that the average ________ (A.. Has. B. Has not) increased and the probability that our conclusion is correct is at least ________ percent.

Answer 1

Solution :

= 100000

= 103157

s= 27498

n = 200

To perform this study we should form a null hypothesis stating that the average is

B. less than or equal to

This is the right tailed test .

The null and alternative hypothesis is

H₀ :   ≤ 100000

H_a : > 100000

Test statistic = t

= ( - ) / s / n

= (103157 - 100000) /27498 / 200

= 1.624

p(Z > 1.624 ) = 1-P (Z < 1.624 ) = 0.053

P-value = 0.053

= 0.10

p=0.053<0.10 , So we should

Reject the null hypothesis .

Hence, we may conclude that the average has ,  increased and the probability that our conclusion is correct is at least 5.3 percent .