The Population Standard Deviation

1. (10 pts.) In a random sample of 198 people, 170 said that they watched educational television. Find the 92% confidence interval of the true proportion of people who watched educational television.2.(20 pts.) A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing illegal issues. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%?3. (20 pts.) A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the population is 0.6 miles per hour. At = 0.05, is there enough evidence to reject the claim? Use the P-value method. 4. (20 pts.) A medical investigation claims that the average number of infections per week at a hospital in South Western Pennsylvania is 16.3. A random sample of 10 weeks had a mean number of 17.7 infections with a standard deviation of 1.8. Is there enough evidence to reject the investigator’s claim at = 0.05. Assume the variable is normally distributed. Use the P-value method.4. (20 pts.) A medical investigation claims that the average number of infections per week at a hospital in South Western Pennsylvania is 16.3. A random sample of 10 weeks had a mean number of 17.7 infections with a standard deviation of 1.8. Is there enough evidence to reject the investigator’s claim at = 0.05. Assume the variable is normally distributed. Use the P-value method. 5. (10 pts.) It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.21 at the 95% confidence level? The population standard deviation is 1.3. 6. (20 pts.) A researcher conducts a significance test every time she analyses a new data set. Over time, she conducts 100 tests. (a) Suppose the null hypothesis is true in every case. What is the distribution of the number of times she rejects the null hypothesis at the level 0.05 level? (b) Suppose she rejects the null hypothesis in seven of the tests. Is it plausible that the null hypothesis is correct in every case? Explain.

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