Question

In the past, patrons of a cinema complex have spent an average of $2.50 for popcorn and other snacks.  The amounts of these expenditures have been normally distributed.  Following an intensive publicity campaign by a local medical society, the mean expenditure for a sample of 18 patrons is found to be $2.10. The standard deviation is found to be $0.90. At the 0.05 level of significance, does this recent experience suggest a decline in spending? A Type II Error in the context of this problem would be

		saying spending has declined when it has not.
		saying spending has not declined when it has.
		saying spending has not declined when it has not.
		saying spending has declined when it has.
		none of the above.

Answer 1

Step 1:

Ho: = 2.50

Ha: < 2.50

Null hyothesis states that the average spent on popcorn and other snacks is equal to 2.50

Step 2: Test statistics

n= 18

= 2.10

s = 0.90

The t-critical value for a left-tailed test, for a significance level of α=0.05.   tc=−1.74

Since the t stat (-1.886) is in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that there is a declne in the spending.

Type II Error : Ho is false and we fail to reject the Ho

saying spending has not declined when it has.