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# Statistics Module 5A : Hypothesis Tests Population Proportion

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• Statistics Module 5A : Hypothesis Tests Population Proportion

### Hypothesis Tests Population Proportion

To conduct hypothesis tests, p bar from the sampling distribution is the point estimator of the population proportion. This point estimate is compared with the hypothesized population proportion.  First, structure the null and alternative hypothesis to understand if its a single tailed or two tailed test. Calculate sample standard error and test statistic. The value of test statistic is used to calculate the p value.

Hypothesis testing about a population proportion is featured as the difference between sample population proportion and hypothesized sample proportion.

Use Norm. S. Dist to calculate the value using cumulative function. Reject the null hypothesis if the p value is less than the level of significance i.e. 0.05 0r 0.01. Check out the tutorial on Introduction to Standard Normal and Z scores

Remember p-value is the smallest value for which you can reject the null. The alternative hypothesis is always the research hypothesis.

Critical value tests can also be used with details mentioned below. Alpha (α) : level of significance

### Solved Problem: Hypothesis Tests Population Proportion

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% plan to provide holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.

1. How many business owners in the survey plan to provide a holiday gift to their employees this year ?

2. Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts had decreased from last year.

3. Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? What is the smallest level of significance for which you could draw such a conclusion?  (Statistics for Business & Economics by Anderson, Sweeney, Williams, Camm and Cochran)