Question

Professors in the Economics Department at Western want to determine how challenging the program was for students. Out of a random sample of 21 students, 16 indicated that the program was either "challenging" or "very challenging". The 95% confidence interval estimating the proprotion of all students in the department who thought the program was challenging is given by which of the following?

Question 9 options:

1)	( 0.60903 , 0.91478 )

2)	( -0.57974 , 0.94407 )

3)	( 0.66896 , 0.85485 )

4)	( 0.57974 , 0.94407 )

5)	( 0.05593 , 0.42026 )

Question 10 (1 point)

A local pizza place claims that they average a delivery time of 6.33 minutes. To test this claim, you order 15 pizzas over the next month at random times on random days of the week. You calculate that the average delivery time is 8.99 minutes with a standard deviation of 1.268 minutes. You create a 95% confidence interval of (8.29, 9.69). Of those listed below, what is the best conclusion you can make?

Question 10 options:

1)	We cannot determine the proper interpretation based on the information given.

2)	The average delivery time does not significantly differ from 6.33 minutes.

3)	You are 95% confident that the average delivery time is less than 6.33 minutes.

4)	The percentage of pizzas that arrive around 6.33 minutes is 95%.

5)	You are 95% confident that the average delivery time is greater than 6.33 minutes.

Answer 1

1)

sample proportion = 16 / 21 = 0.7619

95% Confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.7619 - 1.96 * sqrt( 0.7619 * 0.2381 / 21) < P < 0.7619 + 1.96 * sqrt( 0.7619 * 0.2381 / 21)

0.57974 < p < 0.94407

95% CI is (0.57974 , 0.94407 )

2)

Since 6.33 not contained in confidence interval, we have sufficient evidence to reject null hypothesis.

We conclude that,

You are 95% confident that the average delivery time is greater than 6.33 min