SOLUTION: The depot is using a standard of 650 hours for a particular modification effort. You are to review the standard and determine whether it should be revised. After sampling 20 of the

Question 1030964: The depot is using a standard of 650 hours for a particular modification effort. You are to review the standard and determine whether it should be revised. After sampling 20 of these modifications you calculate a mean of 665 hours and a standard deviation of 45 hours. We are concerned that the hours might be higher or lower than the 650 hour standard. Test the standard at the .05 level of significance. Select the correct answer out of each pair of choices. (Carry intermediate calculations to three decimal places.)
The tp is 2.093

The tp is 1.729

The tc is 1.491

The tc is 2.981

We would fail to reject the null hypothesis

We would reject the null hypothesis

We would recommend using the existing standard.

We would recommend revising the standard.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The problem uses a p-value test of 0.05
:
The two-tailed hypothesis test is the common one to use
:
H1 is the hours may be higher or lower than the standard 650
Ho is there is no difference with the standard
:
We will work with the 95% confidence level and alpha = 0.05
Since this is a two-tailed test, we use 0.05 / 2 = 0.025
:
Since we do not have the standard deviation for the population, we will use the student t-statistic distribution
:
t-statistic = (Sample mean - population mean)) / (Sample std.dev. / square root(Sample size) = (655 - 650) / (45 / square root(20)) = 0.496903995 approx 0.497
:
Degrees of Freedom = Sample size - 1 = 20 - 1 = 19
:
Consulting the student t-tables, we find the critical value is 2.093
:
Our calculated t-statistic is 0.497 which is < 2.093
:
the associated p-value is 0.0046 approx 0.005
:
we can not reject the null hypothesis since 0.005 < 0.05
:
***********************************************
tp is 2.093
not sure of your definitions of tp and tc
We would fail to reject the null hypothesis
We would recommend using the existing standard
***********************************************

RELATED QUESTIONS
1) The depot is using a standard of 635 hours for a particular modification effort. You... (answered by Boreal)

The depot is using a standard of 635 hours for a particular modification effort. You are... (answered by stanbon)

The depot is using a standard of 635 hours for a particular modification effort. You are (answered by lynnlo)

The depot is using a standard of 635 hours for a particular modification effort. You... (answered by lynnlo)

The depot is using a standard of 635 hours for a particular modification effort. You are... (answered by psbhowmick)

Invoices at a particular depot have amounts, which follow a Normal distribution with a... (answered by ewatrrr)

4. In tests of a computer component, it is found that the mean time between failures is... (answered by stanbon)

A mobile phone manufacturer is promoting a new mobile because of its excellent battery... (answered by Boreal)

Scores for a certian professional exam are approximately normally distributed with a mean (answered by ewatrrr)