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6033Week 5 Assignment:

Steps to Hypotheses Testing

(Rubric included)

Instructions

For this Assignment, review this week's Learning Resources, including the 5 step approach to hypothesis testing document. Read the research scenario, below, and then answer the questions related to the steps that must be followed to make the appropriate decision as to reject, or fail to reject, the null hypothesis.

Submit this Application Assignment by Day 7.

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Research Scenario

Sleep deprivation is common in today's society. Sleep duration for the general adult population is estimated to last m = 7.5 hours and s = 0.5 hours.Several studies have shown that anxiety tends to increase the risk for sleep deprivation. Using clinical data, a researcher measured sleep duration for a sample of n = 81 adults suffering from anxiety.Average sleep duration for this sample was x = 6.9 hours.Do these data indicate that adults with anxiety tend to have higher risk for sleep deprivation?Test with p=.05.

Note

= population mean

x = sample mean

s = standard deviation

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Note: Each response is worth 6 points

Step 1: Set up your hypothesis and determine the level of significance

State the null hypothesis

1.In written format

Answer: Anxiety does not increase the risk for sleep deprivation. There is no association between anxiety and the risk of sleep deprivation.

2.In mathematical format

Answer: H₀: = 7.5

State the alternative hypothesis

3.In written format

Answer: Anxiety tends to have a notable increase in the risk for sleep deprivation. There is indeed an association between anxiety and the risk of sleep deprivation.

4.In mathematical format

Answer: : H_A: 7.5

Determine the Level of significance

5.Based on information in the scenario, what is the level of significance to be used?

Answer: alpha = .05. If in this scenario, the confidence is 95% (z= 1.96), the significance level would be = 1- C = 1- 0.95 = 0.05.

Step 2: Select the appropriate test statistic

6.The appropriate test statistic for the above scenario is the one-sample z test. What is a Z test?Describe why this is the appropriate test for the scenario?

Answer: According to Gerstman (2015), under conditions of normal distribution (mean=median=mode), a Z test is a statistical tool used to compares the mean of the sample to the mean of the population when n > 30 and the population standard deviation is known.

The Z test is appropriate for this research scenario because n > 30, and the standard deviation s = 0.5 hours is known.

Step 3: Set up the decision rule

7.Based on the level of significance you set in Step 1 (Question 5) and whether your alternative hypothesis is directional or non-directional, what is your decision rule? (In other words, what is your rejection region?)

Answer: Given that H₀: = 7.5 hrs and = 0.05, the alternative hypothesis is two-tailed and non-directional. This type of hypothesis predicts that there will be a non-specific directional impact on the dependent variable (by the independent variable). Moreover, the region of rejection for H₀is z 1.96 or z -1.96.

Step 4: Compute the test statistic

8.Calculate the z statistic.Please show your work.

Answer: z = (x - ) / ( / n)

Given:

= 7.5

x = 6.9

= 0.5

n = 81

Hence, z = (6.9 - 81) / (0.5 / 81)

z = (-74.1) / (0.5/9)

z = -74.1 / 0.05

z = -1,482

Step 5: Conclusion

9.Do you reject or fail to reject the null hypothesis?

Answer: Given that z = -1,482, and this is less than the region of rejection (z -1.96), the null hypothesis is rejected.

10.Is risk for sleep deprivation affected by anxiety?

Answer: The alternative hypothesis is accepted. Anxiety tends to have a notable increase in the risk for sleep deprivation. There is indeed an association between anxiety and the risk of sleep deprivation.