Chapters 18-19 Summative Assessment

Question

Question 4 

Previous studies have indicated that about 70% of the plants in Delaware are flowering plants, but a botanist in the region suspects the proportion might actually be greater than 70%. The botanist selected a random sample of plants from the region and conducted a test of H₀ : p = 0.7 versus H_A : p > 0.7 and found a p-value of 0.025. Which of the following is a correct interpretation of the p-value?

a	If it is not true that 70 percent of the plants in Delaware are flowering, 0.025 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.
b	If it is not true that 70 percent of the plants in Delaware are flowering, 0.025 is the probability of obtaining a population proportion greater than 0.7.
c	If it is true that 70 percent of the plants in Delaware are flowering, 0.025 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.
d	If it is true that 70 percent of the plants in Delaware are flowering, 0.025 is the probability of obtaining a population proportion greater than 0.7.
e	If it is true that 70 percent of the plants in Delaware are flowering, 0.025 is the probability of obtaining a sample proportion as small as or smaller than the one obtained by the botanist.

Question 5 

A 90% confidence interval is found to estimate the proportion of residents in Kent County, Delaware who plan to vote in an upcoming election. Initially, a sample of 4,000 residents was used. What would be the relationship between the width of the original confidnece interval and the width of a new 90% confidence interval that used a sample of 1,000 residents?

a	The second confidence interval would be 4 times as wide as the original confidence interval.
b	The second confidence interval would be 1/2 as wide as the original confidence interval.
c	The second confidence interval would be 2 times as wide as the original confidence interval.
d	The second confidence interval would be 1/4 as wide as the original confidence interval.
e	The width of the second confidence interval would be equal to the width of the original confidence interval.

Answer 1

Question 4: c. p-value is based on the assumption that the null hypothesis is true and defines probability of obtaining the sample value base on that assumption.

Question 5. c. sqrt(4000) and sqrt(1000) are in denominator of standard error computation, so the smaller the sample size, the larger the standard error and hence the confidence interval. If all else is held constant, the ratio of the 2nd confidence interval to the first would be sqrt(4000/1000) = sqrt(4) = 2.