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 different from 0.5. Assume that sample data consists of 45 girls in 81 births, so the sample statistic of 5/9 results in a z score that is 1 standard deviation below 0. Complete parts (a) through (h) below.

**a.** Identify the null hypothesis and the
alternative hypothesis.

**b.** What is the value of α?

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

Normal distribution

Student (t) distribution

χ2

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

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

**f.** What is the P-value?

**g.** What are the critical value(s)?

**h.** What is the area of the critical
region?

Answer #1

n = 81, x = 45

p̄ = x/n = 45/81 = 0.5556

**a.** Null and alternative hypothesis:

H_{o} : p = 0.5

H_{1} : p ≠ 0.5

**b.** α = **0.01**

**c.** Sampling distribution of the sample
statistic:

**Normal distribution**

**d.** It is a **two-tailed
test.**

**e.** Test statistic:

z =(p̄ -p)/(√(p*(1-p)/n)) = **1**

**f.** p-value = 2*(1-NORM.S.DIST(ABS( 1, 1) =
**0.3173**

**g.** Critical values :

At α = 0.05, two tailed critical value, z_{c} =
NORM.S.INV( 0.05 /2 ) = **± 1.96**

**h.** Critical region:

**Reject if z < -1.96 or z > 1.96**

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