Conduct Hypothesis Tests on the following make sure to follow the steps to guide

Question

Conduct Hypothesis Tests on the following make sure to follow the steps to guide you:

1. State the hypothesis (e.g. Alternative Hypothesis-There is an effect; Null Hypothesis-There is no effect)

2. Locate the critical region

3. Calculate the test statistic

4. Make a decision regarding the Null Hypothesis (e.g. Reject the Null Hypothesis; Fail to reject the Null Hypothesis) and explain what the results mean in terms of the question.

Q2: Reports indicate that graduating seniors in a local high school have an average (m) reading comprehension score of 72.55 with a standard deviation (s) of 12.62. As an instructor in a GED program that provides alternative educational opportunities for students, you’re curious how seniors in your program compare. Selecting a sample of 25 students from your program and administering the same reading comprehension test, you discover a sample mean (X) of 79.53. Assume that you’re working at the .05 level of significance.

a. State an appropriate null hypothesis.

b. What is the value of the calculated test statistic (Z)?

c. State your conclusion.

Q4: The mean (m) educational level for adults in a community is reported as 10.45 years of school completed with a standard deviation (s) of 3.8. Responses to a questionnaire by a sample of 40 adult community residents indicate a mean educational level (X) of 11.45. Assume that you’re working at the .05 level of significance.

a. State an appropriate null hypothesis

b. What is the value of the calculated test statistic (Z)?

c. State your conclusion.

Q5: The historical mean level of production workers at an industrial plant is shown to be 155 units produced per day, with a standard deviation of 15. Following the introduction of a new flextime worker option, a sample of productivity reports for 100 flextime workers reveals a sample mean (X) of 160. Assume that you’re working at the .05 level of significance.

a. State an appropriate null hypothesis.

b. What is the value of the calculated test statistic (Z)?

c. State your conclusion.

Explanation / Answer

4)

a) Hypothesis;

Null hypothesis Ho: mean = 10.45

alternative hypothesis Ha: mean = not equal to 10.45

n = 40 , std. deviatin = 3.8 , x = 11.45

b) Test statistic:

z = ( x - mean) / (s/ sqrt(n))

= (11.45 - 10.45) / (3.8/ sqrt(40))

= 1.67

we need to find p value by using z statistic value at 0.05 leval of significance

p value =  0.094919

Here, p value > 0.05

c) Conclusion, So, we do not reject the null hypothesis

5)

a) Hypothesis;

Null hypothesis Ho: mean = 155

alternative hypothesis Ha: mean = not equal to 155

n = 100 , std. deviatin = 15 , x = 160

b) Test statistic:

z = ( x - mean) / (s/ sqrt(n))

= (160 - 155) / (15/ sqrt(100))

= 3.33

we need to find p value by using z statistic value at 0.05 leval of significance

p value = 0.000868.

Here, p value < 0.05

c) Conclusion,

so, we reject the null hypothesis.

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