Question

The Basic Steps to Calculating a Hypothesis Test

You want to start by determining whether you are interested in working with a mean or a proportion. Then identify each of the parts listed below.

1. In order to use the formulas for a hypothesis test we first need to confirm that the sample size requirements for the central limit theorem are satisfied. See the notes for more information. If the sample size is not met acknowledge that you need to proceed with caution.
2. Identify the null and alternative hypotheses. The null hypothesis will be listed first. When working with a proportion the hypothesis will include that symbol for the population proportion, p. When working with a mean the hypothesis will include that symbol for the population mean, µ.
3. Calculate the appropriate test statistic. When working with proportions you will calculate a z-statistic. When working with means you will calculate a t-statistic.
4. Compare your test statistic to the appropriate distribution to find the p-value.
5. Conclude the test in context of the problem.

For each of the four problems below provide all of the steps listed above. Complete all of the work by hand and show your work. You may use the applications listed in the notes to check your work.

1. Suppose a consumer group claims that the proportion of households that have 2 working adults is 80%. An employment agency has reason to believe that the proportion differs from 80%. Before the employment agency starts a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 124 of the households have 2 working adults. Perform the test at the 10% significance level.

Answer 1

condition met:

np>5 and n(1-p)>5
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Ho :   p =    0.8                  
H1 :   p ╪   0.8       (Two tail test)          
                          
Level of Significance,   α =    0.10                  
Number of Items of Interest,   x =   124                  
Sample Size,   n =    150                  
                          
Sample Proportion ,    p̂ = x/n =    0.8267                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0327                  
Z Test Statistic = ( p̂-p)/SE = (   0.8267   -   0.8   ) /   0.0327   =   0.8165
                             
                          
p-Value   =   0.4142 [excel formula =2*NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis                       
There is not enough evidence to say that the proportion differs from 80%

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