The mean age of a sample of 23 people who were playing the slot machines is 48.8

Question

The mean age of a sample of 23 people who were playing the slot machines is 48.8 years, and the standard deviation is 6.8 years. The mean age of a sample of 31 people who were playing roulette is 55.4 with a standard deviation of 3.2 years. Can it be concluded at alpha = 0.10 that the mean age of those playing the slot machines is less than those playing roulette? Use psi_1 for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. State the hypotheses and identify the claim with the correct hypothesis. This hypothesis test is a one-tailed test. Find the critical value(s). Round the answer to three decimal places. Critical value is 1.321. Compute the test value. Round the answer to 3 decimal places.

Explanation / Answer

The statistical software output for this problem is:

Two sample T hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(without pooled variances)

Hypothesis test results:

Hence,

Test value = - 4.314

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -6.6 1.5299534 29.244338 -4.3138569 <0.0001

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