In: Statistics and Probability
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.
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