Question

a)In order to determine the average price of hotel rooms in georgia, a sample of 63 hotels were selected. It was determined that the test statistic (z) was $1.74. We would like to test whether or not the average room price is significantly different from $110. Population standard deviation is known to us.Compute the p-value.

b)In order to determine the average price of hotel rooms in Atlanta, a sample of 36 hotels were selected. It was determined that the average price of the rooms in the sample was $108.4. The population standard deviation is known to be $13. We would like to test whether or not the average room price is significantly different from $110.Compute the test statistic.

c)A sample of 36 account balances of a credit company showed an average balance of $1,179 and a standard deviation of $136. You want to determine if the mean of all account balances is significantly greater than $1,150. Use a 0.05 level of significance. Assume the population of account balances is normally distributed.Compute the test statistic.

Answer 1

Solution:

a)

n = 63

test statistic (z) = $1.74

two tailed test

P-value = 0.0819

P-value > = 0.05 , fail to Reject H0

the average room price is not significantly different from $110

b)

= $108.4

= $13

n = 25

Hypothesis:

H0 :     $110

Ha : $110

Test Statistic:

   Z = ( - ) / ( /n)

   Z = (108.4- 110) / ( 13/ 25)

  Z = -0.615

P-value = 0.539

P-value > = 0.05 , fail to Reject H0

the average room price is not significantly different from $110

c)

= $1,179

s = $136

n = 36

a.) Hypothesis:

H0 : $1,150

Ha :   $1,150

Test Statistic:

t = ( - ) / (s /n)

t = (1,179- 1,150) / ( 136/ 36)

t = 0.153

P - value = 0.4396

P-value > = 0.05 , fail to Reject H0

the mean of all account balances is not significantly greater than $1,150.