STAB22H3 Lecture Notes - Lecture 12: Random Variable, Sample Size Determination, Null Hypothesis

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Let and be the two population proportions of successes. Population population proportion sample size count of successes sample proportion. The estimate of the difference in the population proportions is. A ( ) ci for is where is the value for the standard normal density curve with area between and . The standard error of is and the margin of error for confidence level is . Use this method for 90%, 95%, or 99% confidence when the number of successes and the number of failures in each sample are at least 10. Example: let"s find a 95% ci for the difference between proportion of men and of women who are frequent binge drinkers. n. Report: men are 5. 4% more likely to be binge drinkers with me = 1. 5%. Plus four ci for a difference in proportions. We add 1 success and 1 failure to each sample:

Related Questions

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion

(b) The population proportion

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(d) the z distribution must be used to obtain the critical value.

periwinkleyellowjacket100

Never forget that even small effects can be statistically significant if the samples are large. During a three-year period, 8 of the 57 headed by men and 6 of the 35 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the p-value for the hypothesis that the same proportion of women's and men's businesses fail. (Use two-sided alternative). What can we conclude (use alpha as 0.05)?

The p-value was ___________ so we conclude that ____________.

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is 180 out of 1050 businesses headed by women and 240 out of 1710 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The p-value was ___________ so we conclude that ____________.

c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a p-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses that fail for the settings of both (a) and (b).

Interval for smaller samples: ___________ to ___________.

Interval for larger samples: ___________ to ___________.

What is the effect of larger samples on the confidence interval?

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STAB22H3 Lecture Notes - Lecture 12: Random Variable, Sample Size Determination, Null Hypothesis

STAB22H3 Full Course Notes

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