A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.1, and the sample standard deviation, s, is found to be 4.9. (a) Construct a 96% confidence interval about u if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 68. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error. E?

Engineers designing the next generation of space shuttles plan to include two fuel pumps—one active, the other in reserve. If the primary pump malfunctions, the second is automatically brought on line. Suppose a typical mission is expected to require that fuel be pumped for at most 50 hours. According to the manufacturer's specifications, pumps are expected to fail once every 100 hours. What are the chances that such a fuel pump system would not remain functioning for the full 50 hours?

Suppose that a random sample of 11 adults has a mean score of 79 on a standardized personality test, with a standard deviation of 7 . (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 90% confidence interval for the mean score of all takers of this test. Then find the lower limit and upper limit of the 90% confidence interval

If a school district takes a random sample of 56 Math SAT scores and finds that the average is 488, and knowing that the population standard deviation of Math SAT scores is intended to be 100. Find a 99% confidence interval for the mean math SAT score for this district._____<μ<_____

In a local store a produce manager needs to estimate the mean weight of Texas oranges delivered from farms. In a random sample of 68 oranges, the mean weight is found to be 154 grams. The standard deviation is known to be 9 grams, and the population is normally distributed. What are the lower and upper bounds for a 90% confidence interval of the population mean weight of an orange?

A random sample of size 49 from normal population yields, mean = 7.2 and standard deviation = 2.8. The lower bound of a 99 percent confidence interval for population mean is O a. 6.40 O b. 6.53 O c. 6.13 O d. 6.68

Suppose that the height of Asian males aged 35-44 in the United States is normally distributed with a standard deviation of 3 in. Jeremy takes a simple random sample of 16 such men and notices that none of them are unusually tall or unusually short. He then calculates the average of the sample to be 67 in. and is planning on using this to find a 90% z-confidence interval for the true mean height. Can Jeremy use this information to find the z-confidence interval? Complete the following sentences. The population distribution is and the population standard deviation is Therefore, the sample to find a 90% z-confidence interval.

A researcher is interested in studying the use of hypnosis to relieve pain. She took a random sample of 16 subjects and measured their sensory ratings. The mean of the sensory ratings was found to be 7.5 and standard deviation to be 2.3. It is known that the sensory ratings are normally distributed. Construct a 99% confidence interval for the mean sensory ratings of the population.  a) (5.81, 9.19) b) (6.27, 8.73) c) (6.36, 8.64) d) (6.02, 8.98)

A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x=121.3 and the sample standard deviation is found to be x=12.3. Construct a​ 99% confidence interval for the population mean.

A research scholar wants to know how many times per hour a certain strand of virus reproduces. He wants to construct the 80% confidence interval with a maximum error of 0.2 reproductions per hour. Assuming that the mean is 6.4 reproductions and the variance is known to be 5.29, what is the minimum sample size required for the estimate? Round your answer up to the next integer.