The technician compares repair cost for 2 types of microwave ovens,( type 1 and type 2 ).he believes that the repair cost for the type 1 oven is greater than the repair cost for type 2 oven. A sample of  60 type 1 ovens has a mean repair cost of $74.06 with the standard deviation of $16.10 . a sample of 68 type 2 ovens has mean repair cost of $67.73, with a standard  deviation  of $14.70. conduct a hypothesis test of the technicians claim at this 0.1 level of significance. Let u1  be the true mean repair cost for type 1 oven and u2 be the true mean repair cost for a type 2 ovens.1. State the null and alternative hypothesis for the test2.compute the value of the test statistic.  Round to two decimal places.3.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to two decimal places.4.make the decision for the hypothesis test.

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Asked Apr 15, 2019
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The technician compares repair cost for 2 types of microwave ovens,( type 1 and type 2 ).he believes that the repair cost for the type 1 oven is greater than the repair cost for type 2 oven. A sample of  60 type 1 ovens has a mean repair cost of $74.06 with the standard deviation of $16.10 . a sample of 68 type 2 ovens has mean repair cost of $67.73, with a standard  deviation  of $14.70. conduct a hypothesis test of the technicians claim at this 0.1 level of significance. Let u1  be the true mean repair cost for type 1 oven and u2 be the true mean repair cost for a type 2 ovens.

1. State the null and alternative hypothesis for the test

2.compute the value of the test statistic.  Round to two decimal places.

3.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to two decimal places.

4.make the decision for the hypothesis test.

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Expert Answer

Step 1
  1. Hypotheses:

Denote u1 as the true mean repair cost for type 1 ovens and u2 as the true mean repair cost for type 2 ovens. The hypotheses appropriate to the technicians claim are as follows:

Null hypothesis:

H0: u1= u2

That is, the true mean repair cost for type 1 ovens and type 2 ovens are same.

Alternate hypothesis:

H1: u1> u2

That is, the true mean repair cost for type 1 ovens is greater than type 2 ovens.

  1. Compute the values of the test statistics.

The formula for test statistic is,

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Step 2

Where x1-bar and x2-bar are the sample means of type 1 and type 2 ovens respectively, (u1-u2)0 is the difference between hypothesized mean, s1 and s2 are the sample standard deviation of the type 1 and type 2 ovens and n1 and n2 are the two sample sizes and sp the pooled standard deviation.

Substitute x1-bar = 74.06, x2-bar = 67.73, µ0 = 22, s1 = 16.10, s2 = 14.70, n1 = 60, and n2 = 68 in the formula for pooled standard deviation and test statistic formula.

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Step 3

Thus, the value of the test statistics is 2.32.

3. Computing the decision rule for rejecting the null hypothesis.

Degrees of freedom:

For student’s t distribution,

df = n1+ n2– 2= 60+68 – 2= 126.

Critical value:

The critical value is obtained using the Excel formula, “=T.INV (0.90, 126)”

Thus, the critical value of Student’s t is t1-α =t0.90 = 1.29.

Decision rule for Right-tailed test at α = 0.1:

If tcalc > 1.29,  then reject the n...

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