Question

13. 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 greater than 0.5. Assume that sample data consists of 55 girls in 100 births, so the sample statistic of 11/20 results in a z score that is 1 standard deviation above 0. Complete parts (a) through (h) below

A. Identify the null hypothesis and the alternative hypothesis. Choose the correct answer below.

A.Upper H 0​: p ≠0.5

    Upper H 1​: p>0.5

B.Upper H 0​: p=0.5

Upper H 1​: p≠0.5

C.Upper H 0​: p=0.5

Upper H 1​: p<0.5

D.Upper H 0​: p=0.5

Upper H 1​: p>0.5

b. What is the value of α​?

a=

​(Type an integer or a​ decimal.)

c. What is the sampling distribution of the sample​ statistic?

Student​ (t) distribution

Normal distribution.

X²

d. Is the test​ two-tailed, left-tailed, or​ right-tailed?

Left-tailed

Two-tailed

Right-tailed

e. What is the value of the test​ statistic?

The test statistic is____

​(Type an integer or a​ decimal.)

f. What is the​ P-value?

The​ P-value is____

​(Round to four decimal places as​ needed.)

G. What are the critical​ value(s)?

The critical​ value(s) is/are____

​(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 ____

​(Round to two decimal places as​ needed.)

Answer 1

a)

The null and alternative hypothesis is

D.Upper H 0 : p = 0.5

Upper H 1 : p > 0.5

b)

Level of significance = = 0.01

c)

The sampling distribution of the sample statistic is Normal distribution.

d)

Right-tailed.

Because the alternative hypothesis has greater than sign.

e)

Sample size = n = 100

x = 55

Test statistic is

f)

P-value = P(Z > 1) = 0.1587

g)

Critical value = 2.32

h)

The area > 2.32 is critical region.