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MTH 245 Data assignment 6 , 1 sample hypothesis tests. (50 pts )

Data assignment 6 will only use Samples 2 and 3 that you downloaded at the

beginning of Data Assignment 5. If you don’t have them, download new ones.

These were samples of 50 and samples of 200 students .

UPLOAD SAMPLE 2 (n=50) into StatCrunch then answer Questions 1-3.

Note: your sample will be unique, so it is possible your answers to all 6 questions will

be different from your friend’s.

(15 ) 1. Conduct a test of the null hypothesis that the mean AGE for all students in

the Census at School database is equal to 12 yrs vs the alternative that the mean

AGE is greater than 12 yrs. Use a significance level of 0.05.

Select Stat/ t stats / 1 sample/ with data. Column is AGE. Fill in the appropriate

options for null mean and direction of test .

Provide the Statcrunch output table and an explanation of the results ( Is there

statistically significant evidence for the alternative hypothesis?)

Your answer should include the output table and a sentence like

“There (is / is not ) statistically significant evidence for the mean AGE being

greater than 12 yrs the p value of xxxxxx is (less than / greater than ) the

significance level of xxxxx.”

With correct answers chosen and correct values substituted for xxxxx.

( 5) 2. Suppose you somehow find out that the actual mean AGE for the entire

database population is 13 yrs 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. 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).

(5) 3. Suppose you somehow find out that the actual mean AGE for the entire

database population is 12 yrs. 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. Explain.

UPLOAD SAMPLE 3 (n=200) into StatCrunch then answer Question 4-6.

(15) 4. Conduct a test of the null hypothesis that the proportion of all students in

the Census at School database who are Male 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 is GENDER and Success is

‘M’. Fill in the appropriate options for null proportion and direction of test .

Provide the StatCrunch output table and an explanation of the results ( Is there

statistically significant evidence for the alternative hypothesis?) You should

have a sentence similar to your answer to question 1 , but with the proper

context for this question.

(5) 5. Suppose you somehow find out that the actual proportion of males for the

entire database population is 50%. Looking back at your test from question 4, was

the result of your test a correct decision, a Type I error, or a Type II error. Explain.

(5) 6. Suppose you somehow find out that the actual proportion of males for the entire

database population is 48 %. Looking back at your test from question 4, was the

result of your test a correct decision, a Type I error, or a Type II error. Explain.

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Tags:

null hypothesis

proportion of successes

sample hypothesis tests

database population

Hypothesis test

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