Question

In: Statistics and Probability

When the background music was slow, the mean amount of bar purchases for a sample of...

When the background music was slow, the mean amount of bar purchases for a sample of

17 restaurant patrons was $30.47 with a standard deviation of $15.10. When the background

music was fast, the mean amount of bar purchases for a sample of 14 patrons in the same

restaurant was $21.62 with a standard deviation of $9.50.

(a) Assuming equal variances, at a significance level

α=.01, is the mean amount of bar purchases higher when the music is slow?

(b) Calculate the p-value.

Solutions

Expert Solution

The null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 > μ2

Assume that the population having equal variances, so we used pooled standard deviation.

Using TI-83 plus calculator we get,

Test statistic = t = 1.902

Degrees of freedom = 17 + 14 - 2 = 29

Critical value = 2.462

Since, test statistic = 1.902 < 2.462, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to conclude that, the mean amount of bar purchases higher when the music is slow.

p-value = TDIST(1.902, 29, 1) = 0.0336

=> p-value = 0.0336


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