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Ch. 21 Practice

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A report on unemployment from last year found that 11% of Americans were out of work at some point in the year. A random sample of 1430 Americans was taken and found that 136 were (a) Does this indicate that Americans are finding more jobs this year? Use a 5% level of significance. H0: p = % of Americans are unemployed this year. HA: p < .11 Less than 11% of Americans are unemployed this year.

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**All conditions have been met to use the Normal model for a 1-proportion z-test.**

Mechanics: P-Value = P(z < ) =

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Conclusion: Since the P-Value is less than alpha( < 0.05), we reject the null hypothesis. There is statistically significant evidence that the proportion of Americans that are unemployed is less than 11%. (b) Explain what the P-Value means in this context. There is a 3.6% chance of getting a sample proportion of 9.5% or lower if the true proportion of Americans that are unemployed is truly 11%.

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**(c) 95% Confidence interval:**

All conditions have been met to use the Normal model for a 1 proportion z-interval. We are 95% confident that the true proportion of Americans that are unemployed lies between 7.99% and 11.03%. (d) Does the conclusion from the confidence interval confirm or contradict your conclusion to the hypothesis test? Explain. It contradicts since 11% falls within the interval.

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(e) What should the confidence level have been for the interval to match the significance level for the test? Does the interval created match the conclusion now? Since it was a 1 Sided test and alpha was 5%, should have used a 90% Confidence Level. Now 11% does not fall within the interval. (f) What level of significance would match the 95% confidence level? What would the conclusion to the hypothesis test be if that level of significance was used? α = 0.025, Fail to reject

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**(g) What is a Type I Error in this context?**

We stated that the proportion of Americans that are unemployed is less than 11% when it is still 11%. (h) What is a Type II Error in this context? We stated that the proportion of Americans that are unemployed is not less than 11% when it is less than 11%. (i) Describe what power means in this context. Power is the probability that we stated that the proportion of Americans that are unemployed is less than 11% when it is less than 11%.

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**(j) Suppose that a new sample was taken with 621 Americans**

(j) Suppose that a new sample was taken with 621 Americans. A new test is run with the same level of significance(5%). How would the Type I Error, Type II Error, and Power be affected by this change? Type I Error – Remains the same Type II Error – Increases Power – Decreases

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Statistical Inference Drawing conclusions (“to infer”) about a population based upon data from a sample. Drawing conclusions (“to infer”) about a population.

Statistical Inference Drawing conclusions (“to infer”) about a population based upon data from a sample. Drawing conclusions (“to infer”) about a population.

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