Question

PLEASE ANSWER ALL QUESTIONS !

1. Gwen suspects fraud is occurring at a hotel she manages. Historically, each of her hotels spends $8,250 per month in maintenance expenses with a standard deviation of $1,070. At the suspect hotel, the last 31 months have averaged $8,490 in maintenance expenses. Gwen thinks the hotel is spending significantly more than the others. Use the 10% significance level.

Calculate the value of the test statistic.

Select one:

a. 0.87

b. 0.89

c. 1.36

d. 1.25

e. 1.54

2. Harley is working as a waiter at a restaurant while paying his way through school. The manager told him he could expect $95 per night in tips with a standard deviation of $30. However, after 32 nights he is averaging only $85 in tips. He wants to know if this is significantly different at the 5% significance level.

Calculate the value of the test statistic.

Select one:

a. -2.06

b. -1.61

c. -1.89

d. -2.26

e. -2.64

Answer 1

Solution :

1) The null and alternative hypothesis is,

H₀ :   = 8250

H_a : > 8250

= 8490

s = 1070

n = 31

Test statistic = t =

= ( - ) / / n

= (8490 - 8250) / 1070 / 31

Test statistic = t = 1.25

correct option is = d

2) The null and alternative hypothesis is,

H₀ :   = 95

H_a :     95

= 85

s = 30

n = 32

Test statistic = t =

= ( - ) / / n

= (85 - 95) / 30/ 32

Test statistic = t = -1.89

correct option is = c