Question

1. A real estate manager wants to test if the population correlation between lot value and lot size is different from zero. According to the manager's calculations, the p-value is 0.002.

Select the correct conclusion from the following choices.

Group of answer choices

a. With a p-value of 0.002, we have strong evidence that the true correlation between lot value and lot size is different from zero.

b. With a p-value of 0.002, we have no statistically significant evidence that the true correlation between lot value and lot size is different from zero.

c. With a p-value of 0.002, we have strong confidence that the sample correlation between lot value and lot size is different from zero.

d. With a p-value of 0.002, we have no statistically significant evidence that the sample correlation between lot value and lot size is different from zero.

2. For the same value of x, which is wider, a 95% confidence interval or a 95% prediction interval?

Group of answer choices

a. 95% prediction interval

b. 95% confidence interval

c. They have the same width

d. We cannot compare the widths of confidence intervals and prediction intervals

3. A college football scout was interested in seeing if a football players height was a good predictor of how fast they were. He randomly sampled 15 different football players and recorded both their heights and their 40 yard dash times. For a person that was 6 ft 3 in tall, he computed a 99% confidence interval for mean speed to be (4.4, 4.8).

Which of these options below is the best interpretation of this confidence interval?

Group of answer choices

a. It can be stated with 99% confidence that the mean speed for players who are 6 ft 3 in tall is between 4.4 and 4.8 seconds.

b. 99% of the time a player will run the 40 yard dash in between 4.4 and 4.8 seconds.

c. 99% of all players are 6ft 3in tall.

d. It can be stated with 99% confidence that out of the 15 football players sampled those who were 6ft 3in tall averaged between 4.4 and 4.8 seconds in the 40 yard dash.

Answer 1

Solution:

1) Based on p-value we make decision rule as follows:

If p-value is less than the significance level, then we reject the null hypothesis and conclude that we have strong evidence that correlation between the two variables is different from zero.

If p-value is greater than the significance level, then we fail to reject the null hypothesis and conclude that we do not have enough evidence that correlation between the two variables is different from zero.

For the given scenario the null and alternative hypotheses will be as follows:

i.e. The population correlation between the lot value and lot size is zero.

i.e. The population correlation between the lot value and lot size is not zero.

p-value = 0.002

Generally significance level of 0.05 or 0.01 is used.

Our p-value is 0.002 which is less than the significance level of 0.01. Therefore we shall reject the null hypothesis.

Hence, with a p-value of 0.002, we have strong evidence that the true correlation between lot value and lot size is different from zero.

Option (a) is correct.