Question

1. Write down the null hypothesis.
2. Write down the alternative hypothesis.
3. Explain why you chose your hypotheses as such.
4. Do a hypothesist test of your data at the α = 2% level of significance for the population proportion by carrying out the following five steps:
5. View an example of how to use StatCrunch to compute the value Z_α
   If it is a left-tailed test, what is the critical value, -z_0.02?
   If it is a right-tailed test, what is the critical value, z_0.02?
   If it is a two-tailed test, what are the two critical values, ±z_0.01?
6. Write down the test statistic, z₀.
7. Write down the P-value.
8. Write down the sample size.
9. Write down the sample proportion.
10. Use the classical method to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.
11. Use the P-value to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.
12. Does the conclusion make sense to you? why or why not?

One sample proportion hypothesis test:

Outcomes in : Gender
Success : Female
p : Proportion of successes
H₀ : p = 0.5
H_A : p ≠ 0.5

Hypothesis test results:

Variable	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
Gender	399	697	0.57245337	0.01893885	3.8256478	0.0001

Answer 1

Null hypothesis is H₀ : p = 0.5
Alternate hypothesis is H_A : p ≠ 0.5

Null hypothesis is what we believe to be true before the test, and the alternate hypothesis is the test used to research from a given sample that if there is a difference in what the belief was from actual value.

Thus p=0.5 is what is believed to be true.

and p ≠ 0.5 is what we have to research.

Since there is an inequality sign in the alternate hypothesis, a two tailed test is required.

The conclusion is in consensus to the sample which has been tested at a very small significance level. Hence, it does make sense.