Normal Distribution, Test of Hypothesis, Correlation

The population data is normally distributed with a mean of 30 and a standard deviation of 5. Find the following Z-statistics and associated probabilities.

1. P(17 < X < 26)

2. P( X < 32)

A population of yearly average rainfall for the Amazon jungle is normally distributed with a mean of 1000 inches and a standard deviation of 200. If we draw a sample of 16 find the probabilities of:

3. P( X > 1,050)

4. P( X < 960)

5. A random sample of 200 observations from a normal population whose population standard deviation is 100 produced a mean of 150. Does this provide enough evidence with a 95% confidence to infer that the population mean is less than 160?

Ho: µ < 160
Ha: µ > 160

6. Determine if there is enough statistical evidence with 99% confidence to infer that the population mean is greater than 50. The sample mean is 55, with a sample size of 25 and a population standard deviation of 10.

Ho: µ > 50
Ha: µ < 50

7. In a random sample of 29 observations from a normal population, we found that the sample mean is 77, and the sample standard deviation is 3. With a confidence level of 99% test the hypothesis.

Ho: µ = 75
Ha: µ not equal to 75 (not equal)

8. In a random sample of 10 observations from a normal population, we found that the sample mean is 11,500 and the sample standard deviation is 3,000. With a confidence level of 95%, test the hypothesis:
Ho: µ < 10,000
Ha: µ > 10,000

9. A bank is interested in determining whether their customer's checking balances are linearly related to their savings balances. A sample size of 20 customers was selected and the correlation was calculated to be +.40. The bank is interested in testing to see whether there is a significant linear relationship between the two variables at a 95% confidence level.
Ho: rho = 0
Ha: rho > 0

10. Given the three states of correlation, explain how two data sets would move with each other in that state.

-1:

0:

+1:

11. A medical research team is developing a new kind of typhoid shot. The old typhoid shot was known to protect the population for a mean of 6 months with a standard deviation of 3 months. To test the variability of the new shot, a random sample of 24 people was given the new shot. Regular blood tests showed that the sample standard deviation of protection time was 1.9 months. Using a .05 level of significance, test the claim that the new typhoid has a smaller variance of protection times.
Ho: (standard deviation squared) =9
Ha: (standard deviation squared) > 9

12. USA Today reported that about 47% of the general consumer population in the U.S. is loyal to the automobile manufacturer of their choice. Suppose that Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%. Use a level of significance of .01

Ho: p = .47
Ha: p > .47