Question

A local casino operator was interested in finding ways to attract younger customers and decided to analyze the ages of customers playing different games. A sample of 25 people playing the slot machines had an average age of 48.7 years with a standard deviation of 6.8. A sample of 35 people playing the roulette wheel had an average age of 52.4 years with a standard deviation of 3.2.

Can it be concluded that the mean age of those playing the slot machines is less than the mean age of those playing the roulette wheel.

Perform the appropriate hypothesis test (using critical value method) with a significance level of 0.05.

Bonus: Find the p-value for the test and use it to make a conclusion.

**** I am having difficulty finding/calculating the p-value. ****

Answer 1

H₀:

H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                             = (48.7 - 52.4)/sqrt((6.8)^2/25 + (3.2)^2/35)

                             = -2.53

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

     = ((6.8)^2/25 + (3.2)^2/35)^2/(((6.8)^2/25)^2/24 + ((3.2)^2/35)^2/34)

     = 32

At = 0.05, the critical value is t_{0.05, 32} = -1.694

Since the test statistic value is less than the critical value(-2.53 < -1.694), we should reject the null hypothesis.

So at 0.05 significance level, we can conclude that the mean age of those playing the slot machines is less than the mean age of those plaing the roulette wheel.

P-value = P(T < -2.53)

             = 0.0083

Since the P-value is less than the significance level (0.0083 < 0.05), we should reject the null hypothesis.