1) A new type of organic pesticide has been developed and will be marketed if it is at least as effective as its chemical-based competitor.List the null hypothesis, alternate hypothesis, and describe the Type I and Type II errors that could result, in this context. (8 points)

2) A random sample of the organic pesticide has been tested against the chemical-based pesticide and the researcher found a P-value of 0.053.The researcher concludes the organic pesticide is more effective.Explain what the P-value means in this context. (2 points)

3) Five Star Convenience Stores has commissioned Stats-R-Us, a statistical firm, to survey its customers in order to estimate the mean amount spent per customer. From previous records the standard deviation is believed to be = $5.00. In their proposal to Five Star, Stats-R-Us states that they plan to base the estimate for the mean amount spent per customer on a sample size of 100 and use a 95% confidence interval. Five Star's president has suggested that the sample size be increased to 400. If nothing else changes, what effect will this increase in the sample size have on

a.)the point estimate of the mean? (2 points)

b.)the margin of error of estimation? 2 points)

c.)the confidence interval? (2 points)

The CEO of Five Star wants the level of confidence increased to 99%. If nothing else changes, what will this increase in level of confidence have on

d.)the point estimate of the mean? (2 points)

e.)the margin of error of estimation? 2 points)

f.) the confidence interval? (2 points)

4) The standard deviation of a normally distributed population is equal to 10. A sample size of 25 is selected, and its mean is found to be 95.

a.) Find an 80% confidence interval for . (4 points)

b.) If the sample size were 100 what would be the 80% confidence interval? (4 points)

c.) If the sample size was 25 but the standard deviation was 5, what would be the 80% confidence interval? (4 points)

5)The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of childcare to be $689. Assume the population standard deviation to be $40.

a.)Perform the appropriate test of hypothesis for the potential resident using = 0.01. (8 points)

Step 1

Step 2

Step 3

Step 4

c) What effect, if any, would there be on the conclusion in part a.) if you change to 0.05? (3 points)