Question

2) The same liquor store owner wants to do a similar comparison but for high end wines to see if there is a difference. The owner samples 16 white wines finding an average of $45.13 (s=5.10) and samples 16 red wines and finds an average of $48.69 (s=5.23). Use alpha=0.05.

2a) What is the standard error?
2b) What is the test statistic?
2c) What is the p-value?
2d) What can you conclude about cost of high end wines?

Answer 1

2a) The standard error is given by:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

= sqrt[(5.10^2/16) + (5.23^2/16)]

= 2.32

2b) The test statistic is given by:

t = (x1 - x2) / SE

= (45.13 - 48.69) / 2.32

= -1.53

2c) The p-value for a two-tailed test with alpha = 0.05 and degrees of freedom = 30 (n1 + n2 - 2) is 0.1384.

2d) Since the p-value (0.1384) is greater than the level of significance (0.05), we fail to reject the null hypothesis that there is no difference in the cost of high end red and white wines. Therefore, we cannot conclude that there is a significant difference in the cost of high end wines.