Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The sample size for company A is [tex]n_1 = 80[/tex]
The sample size for company B is [tex]n_2 = 60[/tex]
The sample mean for A is [tex]\= x _1 = \$16.75[/tex]
The sample mean for B is [tex]\= x _2 = $16.25[/tex]
The population standard deviation for A is [tex]\sigma_1 = \$1.00[/tex]
The population standard deviation for B is [tex]\sigma_1 = \$ 0.95[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \ne 0[/tex]
Generally the test statistics is mathematically represented as
[tex] z = \frac{ \= x_1 - \= x_2}{ \sqrt{\frac{ \sigma_1^2}{n_1} + \frac{ \sigma_2^2}{n_2} } }[/tex]
=> [tex]z = \frac{ 16.75 - 16.25}{ \sqrt{\frac{ 1.00^2}{80} + \frac{ 0.95^2}{60} } }[/tex]
=> [tex]z = 3.01283186 [/tex]
Generally from the normal distribution table the probability of z
[tex]P(t > z) = 0.0013 [/tex]
Gnerally the p-value is mathematically represented as
[tex]p-value = 2 * P(z > 3.0 )[/tex]
=> [tex]p-value = 2 * 0.0013 [/tex]
=> [tex]p-value = 0.0026 [/tex]
