According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100:114 (46.7% girls). Suppose you don't believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 62 girls and 88 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7? Conduct a hypothesis test at the 5% level.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)
Part (b)
Part (c)
Part (d)
State the distribution to use for the test. (Round your answers to four decimal places.)
P' ~

,

Part (e)
What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

Correct: Your answer is correct.
=
Incorrect: Your answer is incorrect.
Part (f)
What is the p-value? (Round your answer to four decimal places.)

Incorrect: Your answer is incorrect.


Explain what the p-value means for this problem.
If
H0
is false, then there is a chance equal to the p-value that the sample ratio is 62 out of 150 or less OR 78 out of 150 or more.
If
H0
is false, then there is a chance equal to the p-value that the sample ratio is not 62 out of 150 or less OR 78 out of 150 or more.
If
H0
is true, then there is a chance equal to the p-value that the sample ratio is 62 out of 150 or less OR 78 out of 150 or more.
If
H0
is true, then there is a chance equal to the p-value that the sample ratio is not 62 out of 150 or less OR 78 out of 150 or more.
Correct: Your answer is correct.
Correct! A p-value is the probability that an outcome of the data will happen purely by chance when
H0
is true.
Part (g)

Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
=
Incorrect: Your answer is incorrect.


(ii) Decision:
reject the null hypothesis
do not reject the null hypothesis
Correct: Your answer is correct.

(iii) Reason for decision:
Since < p-value, we do not reject the null hypothesis.
Since < p-value, we reject the null hypothesis.
Since > p-value, we reject the null hypothesis.
Since > p-value, we do not reject the null hypothesis.
Correct: Your answer is correct.

(iv) Conclusion:
There is sufficient evidence to conclude that the percent of girls born in China is not equal to 46.7%.
There is not sufficient evidence to conclude that the percent of girls born in China is not equal to 46.7%.
Correct: Your answer is correct.
Part (i)
Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)
WebAssign Plot