Statistics
Choose the correct answer:
1. (10 pts.) Regarding the standard error of the mean, ……. (a) As the sample size decreases, the standard error decreases (b) As the sample size increases, the standard error decreases (c) It is defined as one-half of the population standard deviation (d) As the sample size increases, the standard error increases
2. (10 pts.) As the confidence interval becomes wider, the likelihood that the population mean, ……. (a) Will be in that interval is unchanged (b) Will be contained in that interval increases
(c) Will be in the interval becomes irrelevant (d) Will be contained in that interval decreases
3. (10 pts.) As the sample size increases , …….. (a) The confidence interval becomes more narrow (b) The confidence interval becomes irrelevant (c) The confidence interval is unchanged (d) The confidence interval becomes wider
4. (10 pts.) The risk that the confidence interval does not contain the population mean can be reduced by ……… (a) Decreasing the sample size (b) Increasing the population size
(c) Decreasing the population size (d) Increasing the sample size
5. (10 pts.) The t-distribution is very much like the standard normal distribution except that the t-distribution (a) Has a larger variance (b) Has a smaller standard deviation
(c) Is bi-symmetrical (d) Has a smaller variance
6. (10 pts.) In a random sample of 197 people, 146 said that they watched educational television. Find the 84% confidence interval of the true proportion of people who watched educational television.
7. (15 pts.) A sample of 15 two litter bottles of a soft drink delivers a mean weight of 2009 mlt. with a sample standard deviation of 11 mlt. The quality assurance department wants to determine if there is a true fill problem, so determine the margin of error and confidence interval at 93% confidence.
8. (15 pts.) A researcher claims that the average wind speed in a certain city is 10 miles per hour. A sample of 20 days has an average wind speed of 9.6 miles per hour. The standard deviation of the population is 0.8 mile per hour. At , (a) Determine the null and alternative hypothesis.
(b) Determine the test statistics and P-value. (c) Is there enough evidence to reject the claim? Explain.
9. (10 pts.) It is desired to estimate the mean of the statistics course of each undergraduate class at a large university. How large a sample is necessary to estimate the mean within 0.41 at the 87% confidence level? The population standard deviation is 1.7.
