Question

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $.95 The p-value is a. .0084. b. .0042. c. .0026. d. .0013

Answer 1

The correct option is C

Explanation:

From the question we are told that

The sample size for company A is
`n_1 = 80`

The sample size for company B is
`n_2 =  60`

The sample mean for A is
`\= x _1  = \$16.75`

The sample mean for B is
`\= x _2  =  $16.25`

The population standard deviation for A is
`\sigma_1 =  \$1.00`

The population standard deviation for B is
`\sigma_1 = \$ 0.95`

The null hypothesis is
`H_o :  \mu_1 - \mu_2 = 0`

The null hypothesis is
`H_o :  \mu_1 - \mu_2 \\e 0`

Generally the test statistics is mathematically represented as

`z =  \frac{ \= x_1 - \= x_2}{ \sqrt{( \sigma_1^2)/(n_1) + ( \sigma_2^2)/(n_2) } }`

=>
`z  =  \frac{ 16.75 - 16.25}{ \sqrt{( 1.00^2)/(80) + ( 0.95^2)/(60) } }`

=>
`z  =  3.01283186`

Generally from the normal distribution table the probability of z

`P(t > z) = 0.0013`

Gnerally the p-value is mathematically represented as

`p-value  =  2 *  P(z > 3.0 )`

=>
`p-value  =  2 *  0.0013`

=>
`p-value  =  0.0026`