Question

QUESTION 11

1. A restaurant owner wants to estimate the mean wait time during lunchtime. She knows that the standard deviation of wait times is 14 minutes. Based on this information, how many customers should she sample to get a 90% confidence interval with a margin of error of 2.5 minutes?

   		121
   		120
   		84
   		85

2 points   

QUESTION 12

1. The machinist closely monitors the machine that produces a major part for an airplane engine. In the past, 10% of the parts produced were defective. How many parts should be sampled to obtain a 95% confidence interval with a 0.04 margin of error.

   		217
   		19
   		216
   		20

2 points   

QUESTION 13

1. A two-bedroom rental in a small town was $700 five years ago. As the population in the town has grown, the City Commissioner believes that rents have increased. What is the appropriate set of hypotheses to test this claim?

Answer 1

Solution:

Question 11)

E = 2.5

c = 90%

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

thus

Question 12)

p = 0.10

E = 0.04

c = 95%

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

_{(Sample size is always rounded up)}

Question 13)

A two-bedroom rental in a small town was $700 five years ago.

As the population in the town has grown, the City Commissioner believes that rents have increased.

that is we have to test if:  

thus hypothesis are:

Vs