Question

A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is less less than 0.5. Assume that sample data consists of 45 girls in 100 ​births, so the sample statistic of StartFraction 9 Over 20 EndFraction 9 20 results in a z score that is 1 standard deviation below below 0. Complete parts​ (a) through​ (h) below. Click here to view page 1 of the Normal table. LOADING... Click here to view page 2 of the Normal table. LOADING... a. Identify the null hypothesis and the alternative hypothesis. Choose the correct answer below. A. Upper H 0 H0​: p not equals ≠0.5 Upper H 1 H1​: p less than <0.5 B. Upper H 0 H0​: p equals =0.5 Upper H 1 H1​: p not equals ≠0.5 C. Upper H 0 H0​: p equals =0.5 Upper H 1 H1​: p less than <0.5 D. Upper H 0 H0​: p equals =0.5 Upper H 1 H1​: p greater than >0.5 b. What is the value of alpha α​? alpha α equals = 0.1 ​(Type an integer or a​ decimal.) c. What is the sampling distribution of the sample​ statistic? Normal distribution chi squared χ2 Student​ (t) distribution d. Is the test​ two-tailed, left-tailed, or​ right-tailed? ​Two-tailed Right Right​-tailed Left Left​-tailed e. What is the value of the test​ statistic? The test statistic is 10 10. ​(Type an integer or a​ decimal.) f. What is the​ P-value? The​ P-value is 0.1587 0.1587. ​(Round to four decimal places as​ needed.) g. What are the critical​ value(s)? The critical​ value(s) is/are 1.28 1.28. ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.) h. What is the area of the critical​ region? The area is 0.10 0.10. ​(Round to two decimal places as​ needed.)

Answer 1

Given that, n = 100 and x = 45

sample proportion = x/n = 45/100 = 0.45

a) The null and the alternative hypotheses are,

H₀ : p = 0.5

H₁: p < 0.5

b) the value of alpha α​ = 0.01

c) The sampling distribution of the sample statistic is Normal distribution.

d) This test is left-tailed.

e) Test statistic is,

The value of the test statistic is -1.00

f) P-value = P(Z < -1.00) = 0.1587

p-value = 0.1587

g) Critical value at α​  = 0.01 is, -2.33

h) The area of the critical region is 0.01

Note: If significance level of  α = 0.1 ​then critical value is -1.28 and area of critical region is 0.10