Hypothesis Testing

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jakej78

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Accidentally copied the wrong one that I needed help with...

In the past, patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. The amount 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 $4.20. In a one-tail test at the 0.05 level of significance, does this recent experience suggest a decline in spending? Determine and interpret the p-value for the test.

u =< 5.00
u > 5.00
z = -1.8855
z = 1.645
 
jakej78 said:
Accidentally copied the wrong one that I needed help with...

In the past, patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. The amount 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 $4.20. In a one-tail test at the 0.05 level of significance, does this recent experience suggest a decline in spending? Determine and interpret the p-value for the test.

u =< 5.00
u > 5.00
z = -1.8855
z = 1.645
Click to expand...
The numbers you wrote down are familiar, but I can't tell what you intend them to represent. We need to see more text describing the parameters.

The null hypothesis is that the mean did not change:
H_0 --> mu = 5.00

The alternative hypothesis is that the mean decreased:
H_a --> mu < 5.00

The critical z for a single-ended tail of 0.05 is z_c = 1.645; in this case on the negative side of the mean.

If you take a sample of size N=18, what is the distribution of sample means? What is the observed z, and how does it compare to z_c?

Are you supposed to use a t-test for equality of means?
 
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