Question

These are tough. Can someone please help me with these!!

4. Calculate the Level of Significance for the following test: Ho: μ 56.0 versus Ha: μ > 56.0 Suppose σ-4.5, n = 81 and x. = 56.9 4. 5. According to the Encyclopedia Britannica 2004 Almanac, 27.7% of the babies born in Canada are illegitimate. Ms. Pamela Stewart feels that the true proportion must be less than what the Britannica organization published. She intends to use the results of a survey of 250 birth records to challenge the claim Ho: p -0.277 at the 5% level of significance. a. State the appropriate Ha: b. To three decimal places, compute

Answer 1

Question 4

H₀ : $\mu$ = 56

H_a : $\mu$ >56

$\sigma$ = 4.5

n = 81

$\bar x$ = 56.9

Here standard error of sample mean = $\sigma$ /sqrt(n) = 4.5/sqrt(81) = 4.5/9 = 0.5

Test statsitic

Z = (56.9 - 56)/0.5 = 1.80

Here level of significance = Pr(Z > 1.80) = 1 - Pr(Z < 1.80) = 1 - 0.9641 = 0.0359

so here level of significance is 0.036

Question 5

H₀ : p = 0.277

(a) Appropriate Alternative Hypothesis H_a : p < 0.277

(b) Here standard error of proporion = sqrt [0.277 * (1 - 0.277)/250] = 0.0283

Here

p_c < 0.277 - Z_critical se_p

p_c < 0.277 - 1.645 * 0.0283

p_c < 0.230