Question

Conduct a test of the null hypothesis that the mean height for all students in the Census at School database is equal to 155 cm vs the alternative that the mean Height is greater than 155 cm. Use a significance level of 0.05.

a. State the null and alternative hypotheses.

Ho: m = 155

Ha: m > 155

b. Provide the Statcrunch output table.

Hypothesis test results:

Variable	Sample Mean	Std. Err.	DF	T-Stat	P-value
Height	159.86	1.7311103	49	2.8074468	0.0036

c. Provide an explanation of the results (Is there statistically significant evidence for the alternative hypothesis?) You should reference your P-value in your explanation and explain how this led you to your conclusion.

2. Suppose you somehow find out that the actual mean height for the entire database population is 160 cm.

a. Looking back at your test from question 1, was the result of your test a correct decision, a Type I error, or a Type II error.

b. Explain (for example , did you reject a true null, fail to reject a false null, reject a false null, or fail to reject a true null).

3. Conduct a test of the null hypothesis that the proportion of all students in the Census at School database who take a car to school (column J) is equal to 50% vs. the alternative that the proportion is less than 50%. Use a significance level of 0.05.

Stat / proportion stats / 1 sample/with data . Column J is Travel_to_School and Success is ‘Car’.   Fill in the appropriate options for null proportion and direction of test.

a. State the null and alternative hypotheses.

Ho: p = 0.5

Ha: p < 0.5

b. Provide the Statcrunch output table.

a.     Hypothesis test results:

Variable	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
Travel_to_School	0	50	0	0.070710678	-7.0710678	<0.0001

c. Provide an explanation of the results (Is there statistically significant evidence for the alternative hypothesis?) You should reference your P-value in your explanation and explain how

4. Suppose you somehow find out that the actual proportion for the entire database population is 48 %.

a. Looking back at your test from question 1 3, was the result of your test a correct decision, a Type I error, or a Type II error.

b. Explain.

i need help with the questions in bold please and thank you

Answer 1

1)

c)
since p value=0.0036 < α=0.05 , reject Ho
hence, there is enough evidence to conclude that true mean Height is greater than 155 cm at α=0.05

2)
a)
Type I error is rejecting null hypothesis when it is true , so it not type I error
Type II error is fail to reject false null hypothesis , so it is also not type II error

answer is correct Decision

b)
Decsion is
Reject a false Null

3)
p value is very small and less than α=0.05, so, reject Ho
there is enough evidence to conclude that true proportion is less than 50% at α=0.05

4)
a)
It is a coorect decision