A survey of 90 men found that an average amount spent on St. Patrick's day of $55 with a standard deviation of $18. A similar survey of 86 women found they spent an average of $44 with a standard deviation of $16. When testing the hypothesis (at the 5% level of significance) that men spend more than women on St. Patrick's day, what is the test statistic?

The value of the test statistic is 4.70.

Step-by-step explanation:

The hypothesis for this test can be defined as follows:

H₀: Men do not spend more than women on St. Patrick's day, i.e. μ₁ = μ₂.

Hₐ: Men spend more than women on St. Patrick's day, i.e. μ₁ > μ₂.

The population standard deviations are not known.

So a t-distribution will be used to perform the test.

The test statistic for the test of difference between mean is:

Given:

Compute the value of the test statistic as follows:

Thus, the value of the test statistic is 4.70.

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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