Question

11A. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.

		0.05
		0.103
		0.35
		1.24
		1.67

11B. The alternative hypothesis would be _______.

		the population proportion is less than 0.30
		the population proportion is greater than 0.30
		the population proportion is not equal to 0.30
		the population mean is less than 40
		the population mean is greater than 40

11C. The test would be _______.

		a one-tailed test
		a two-tailed test
		an alpha test
		a finite population test
		a finite sample test

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p =0.30

H_a : p >0.30

= x / n = 50/144=0.3472

P₀ = 0.30

1 - P₀ = 1 - 0.30=0.70

(A)Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.3472 - 0.30/ [(0.30*0.70) /144 ]

z= 1.24

(b)the population proportion is greater than 0.30

(C)a one-tailed test