Statistics
Confidence Intervals and Hypothesis Testing Name:
Math 256, Nelson
1. A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.5 deciliters. Find a 95% confidence interval for the mean of all drinks dispensed by this machine if a random sample of 36 drinks had an average content of 2.25 dl.
2. The heights of a random sample of 50 college students showed a mean of 174.5 centimeters. Assume the standard deviation is 6.9 cm. What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5?
3. How large a sample is needed in #1 above is we wish to be 95% confident that our sample mean will be within 0.3 dl of the true mean?
4. A random sample of 1000 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assume a standard deviation of 8.9 years. Find a 95% confidence interval for the actual average life span.
5. On a certain national school test [pic]and [pic]. A principal claims that her students are above average. She takes a random sample of 75 and finds a mean of 525. Is her claim justified?
6. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assuming a standard deviation of 8.9 years, can we conclude that the actual life span is not 75 years? [pic]
7. A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms. Test the hypothesis that the mean is 8 kg against the alternative that it is less than 8 kg, if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. The standard deviation is 0.8 kg. Use a 0.01 level of significance.
8. A trucking firm doesn’t
Math 256, Nelson
1. A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.5 deciliters. Find a 95% confidence interval for the mean of all drinks dispensed by this machine if a random sample of 36 drinks had an average content of 2.25 dl.
2. The heights of a random sample of 50 college students showed a mean of 174.5 centimeters. Assume the standard deviation is 6.9 cm. What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5?
3. How large a sample is needed in #1 above is we wish to be 95% confident that our sample mean will be within 0.3 dl of the true mean?
4. A random sample of 1000 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assume a standard deviation of 8.9 years. Find a 95% confidence interval for the actual average life span.
5. On a certain national school test [pic]and [pic]. A principal claims that her students are above average. She takes a random sample of 75 and finds a mean of 525. Is her claim justified?
6. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years. Assuming a standard deviation of 8.9 years, can we conclude that the actual life span is not 75 years? [pic]
7. A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms. Test the hypothesis that the mean is 8 kg against the alternative that it is less than 8 kg, if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. The standard deviation is 0.8 kg. Use a 0.01 level of significance.
8. A trucking firm doesn’t