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Chapter 9: Q. 10 (page 537)

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5a percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

localid="1650439913140" a.H0__________

b.Ha __________

Short Answer

Expert verified

a.H0:p=0.095

b.Ha:p<0.095

Step by step solution

01

Given Information

9.5percent of adults in the United States are depressed or have a depressive disease. The goal is to see if the genuine number of people suffering from depression or a depressive disease is less than 9.5percent.

02

Explanation part a

The Null Hypothesis is:

  • H0: The true number of persons who suffer from depression or mental disease is 9.5percent.
  • The Null Hypothesis (H0): It's a declaration that there's no difference between sample means or proportions, or between a sample mean or proportions and a population mean or proportion.
03

Explanation part b

An Alternative Hypothesis is:

  • Ha: The genuine proportion of people suffering from depression or a depressive disease is less than 9.5
  • The alternate hypothesis is as follows: It is the population assertion that contradicts H0, and it is what we conclude when we reject H0
04

Step 4: Conclusion 

For the above data, the null and alternative hypotheses are provided by:

H0:p=0.095

Ha:p<0.095

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