Suppose you wanted to determine if you should reject the null hypothesis that running a playing fast tempo (as opposed to slow) music in your store decreases sales by $100 on average. On 65 randomly selected days with fast tempo music on the average store sales is $2,345 with a sample standard deviation of 45, while on 75 randomly selected days with slow tempo music on the average store sales is $2,555, with a sample standard deviation of 65. What would be the proper t-stat for this hypothesis test?
A) $\frac { 2345 - 2555 } { \sqrt { \frac { 45 ^ { 2 } } { 65 } + \frac { 65 ^ { 2 } } { 75 } } }$
B) $\frac { 2345 - 2555 - 100 } { \sqrt { \frac { 45 ^ { 2 } } { 65 } + \frac { 65 ^ { 2 } } { 75 } } }$
C) $\frac { 2345 - 2555 + 100 } { \sqrt { \frac { 45 ^ { 2 } } { 65 } + \frac { 65 ^ { 2 } } { 75 } } }$
D) $\frac { 2345 - 2555 } { \sqrt { 45 ^ { 2 } + 65 ^ { 2 } } }$

Question

Quizplus · Accepted Answer

The correct formula for the t-statistic is:t = (x̄1 - x̄2 - μ0) / √(s1^2/n1 + s2^2/n2)where x̄1 and x̄2 are the sample means, μ0 is the hypothesized difference in means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.In this case, we have:x̄1 = 2,345x̄2 = 2,555μ0 = -100s1 = 45s2 = 65n1 = 65n2 = 75Plugging these values into the formula, we get:t = (2,345 - 2,555 - (-100)) / √(45^2/65 + 65^2/75)= (2,345 - 2,555 + 100) / √(45^2/65 + 65^2/75)= (2,345 - 2,555 + 100) / √(2,025/65 + 4,225/75)= (2,345 - 2,555 + 100) / √(31.1538 + 56.3333)= (2,345 - 2,555 + 100) / √(87.4871)= (2,345 - 2,555 + 100) / 9.3538= (-210 + 100) / 9.3538= -110 / 9.3538= -11.7674Therefore, the correct answer is C.

Suppose You Wanted to Determine If You Should Reject the Null