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Hypothesis Test for Unemployment Rate Between Two Months

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Your mayor just announced that the local unemployment rate dropped last month from the prior month. It went from 10.5% to 10.4%. Is this a significant drop? Explain.

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Hi there,

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The unemployment rate is a way to estimate the degree of unemployment within a certain area (city, state/province, country). Approximating the number of unemployed people within a given area and dividing by the approximate number of employed people within that same area determine the unemployment rate. The unemployment rate is expressed as a percentage.

When the mayor announced that the unemployment rate had dropped from 10.5% to 10.4%, it is easy to ...

Solution Summary

This solution, comprised of over 350 words, includes a completely worked through answer for a specific statistics question regarding the unemployment rate within a city. Full hypothesis testing is done to determine whether the unemployment rate has changed significantly between two given months.

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Null Hypothesis and Alternative Hypothesis Examples

1. Although opinion polls have long found that about 40% of American adults say they attend religious services last week, this is almost certainly not true.
a. Why might we expect answers to a poll to overstate true church attendance?
b. You suspect strongly that the true percentage attending church in any given week is less than 40%. You plan to watch a random sample of adults and see whether or not they go to church. What are your null and alternative hypotheses?

2. The national unemployment rate in a recent month was 5.4%. You think the rate may be different in your city, so you plan to ask a sample of the city residents about their employment status. To see if the local rate differs significantly from 5.4% what hypothesis will you test?

3. A social scientist is studying the ages of executives in top management positions and thinks that the mean ages of technology executives is lower than that in other business sectors. What data need to be collected? What hypotheses are needed?

4. What null and alternative hypothesis should we use if we want to test the claim that on average children attending elementary schools in a certain metropolitan area are more than two miles from the school which they attend.

5. The manufacturer of a spot remover claims that his product removes 90 percent of all spots. In a random sample, the spot remover removes 11 of 16 stains. Write the null and alternative hypotheses.

6. In a study of the relationship between family size and intelligence, 49 "only children" had an IQ of 101.5 with a standard deviation of 6.7 and 50 "first born children" in two-child families had a mean IQ of 105.9 with a standard deviation of 5.8. Write out the relevant null and alternative hypothesis.

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