Question

A 0.1 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 66 girls in 121 births, so the sample statistic of 6/11 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.

b.what is the value of a?

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

-X²

- Student (t) distribution

- Normal Distribution

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

Given that, n = 121 and x = 66

=> sample proportion = 66/121 = 0.5455

a) The null and alternative hypotheses are,

H0 : p = 0.5

Ha : p > 0.5

b) level of significance = 0.1

c) The sampling distribution of the sample proportion is approximately normal distribution.

d) This is right-tailed test.

e) Test statistic is,

=> Test statistic = 1.00

f) p-value = P(Z > 1.00) = 1 - P(Z < 1.00) = 1 - 0.8413 = 0.1587

=> p-value = 0.1587

g) critical value at significance level of 0.1 is, Z_{​​​​​​crit} = 1.28

=> critical value = 1.28

h) Critical Region : Reject H0, Z > 1.28

Since, p-value > 0.10, we fail to reject the null hypothesis.

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