Question

The producer believes that there is more variety in people's appreciation of comedies, and so he assumes that the two population standard deviations are not equal in this situation. Calculate the test statistic (t) for this test. Give your answer to 3 decimal places.

Answer 1

Complete Question

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Answer:

The value is
`t = 2.51`

Explanation:

From the question we are told that

From the question we are told that

The first sample mean is
`\= x_1 = 71.1`

The first standard deviation is
`\sigma _1 = 19.4`

The second sample mean is
`\= x_2 = 63.4`

The second sample deviation is
`\sigma_2 = 10.5`

The first sample size is
`n_1 = 55`

The second sample size is
`n_2 = 46`

Generally the test statistics is mathematically represented as

`t = \frac{\= x_1 - \= x_2 }{ \sqrt{(s_1^2 )/(n_1) +(s_2^2 )/(n_2) } }`

=>
`t = \frac{71.1 - 63.4 }{ \sqrt{(19.4^2 )/(55)  +(10.5^2 )/(46)   } }`

=>
`t = 2.51`