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- A population is normally distributed

- A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8. What is the probability of each of the following:
- Taking a sample size of ten and obtaining a sample mean of 22 or more
- Taking a sample size of 4 and getting a sample mean of more than 26

- A population has a mean of 50 and a standard deviation of 10. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following?
- Between 48.5 and 52.4
- Between 50.6 and 51.3

- Suppose a random sample of 36 is drawn from a population with a mean of 278. If 86% of the time the sample mean is less than 280, what is the population standard deviation?
- A standard sample size of 81 is drawn from the population with a standard deviation of 12. If only 18% of the time a sample greater than 300 is obtained, what is the mean of the population?
- A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of µ? Construct a 94% confidence interval for µ.

6 A random sample of size 39 is taken from a population of 200 members. The sample mean is 66 V and the population standard deviation is 11. Construct a 96% confidence interval to estimate the population mean. What is the point estimate of the population mean?

- Assuming x is normally distributed; use the following information to compute a 90% confidence interval to estimate µ.

313 320 319 340 325 310

321 329 317 311 307 318

8. If a random sample of 41 items produces a sample mean = 128.4 and s = 20.6 what is the 98% confidence interval for µ? Assume x is normally distributed for the population. What is the point estimate?

9. Use the following data to construct a 99% confidence interval for µ. Assume x is normally distributed. What is the point estimator for µ? Verify your calculator answer by submitting an SPSS print out of the answer.

16.4 17.1 17.0 15.6 16.2

14.8 16.0 15.6 17.3 17.4

15.6 15.7 17.2 16.6 16.0

15.3 15.4 16.0 15.8 17.2

14.6 15.5 14.9 16.7 16.3

10. A survey of appraiser found that the average net income for a sale proprietor is $74,914. Because this survey is now almost 15 years old, a researcher wants to test this figure by taking a random sample of 112 sale proprietor appraisers to determine whether the net income figure has changed. The researcher wants to use the eight steps of hypothesis testing to do so. Assume the population standard deviation of net incomes for sale proprietor Appraiser's is $14,530. (Assume the sample mean (X-bar = $78,695)

n = 112, population standard deviation = $14,530 and U (population mean = $74,914))

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