Math

StatisticsQ&A LibraryThe 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.Question

Asked Apr 15, 2019

16 views

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.

Step 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:

*H*_{0}: u1= u2

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

Alternate hypothesis:

*H*_{1}: u1> u2

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

**Compute the values of the test statistics.**

The formula for test statistic is,

Step 2

Where *x*_{1}-bar and *x*_{2}-bar are the sample means of type 1 and type 2 ovens respectively, (u1-u2)_{0} is the difference between hypothesized mean, *s*_{1} and *s*_{2 }are the sample standard deviation of the type 1 and type 2 ovens and *n*_{1 }and *n*_{2} are the two sample sizes and *s _{p}* the pooled standard deviation.

Substitute *x*_{1}-bar = 74.06, *x*_{2}-bar = 67.73, µ_{0 }= 22, *s*_{1} = 16.10,* s*_{2} = 14.70, *n*_{1} = 60, and *n*_{2} = 68 in the formula for pooled standard deviation and test statistic formula.

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...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flyi...

A: (a) Poisson distribution:It is a discrete probability distribution that models the number of events ...

Q: The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample sta...

A: Sample proportion:It is given that out of 420 peas, 116 of them having yellow pods.The claim states ...

Q: This study investigated the cognitive effects of stimulant medication in children with Attention-Def...

A: Solution:The appropriate statistical analysis to determine if there is an effect of drug dose on CPT...

Q: The state superintendent of schools consistently states that the average salary of all substitute te...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

Q: Suppose x has a distribution with μ = 60 and σ = 17. (a) If random samples of size n = 16 are select...

A: Note:Hi there! Thank you for posting the question. The Part (b) of your question asks about the “x d...

Q: D, E, F

A: In this question, we have the data for two groups and we have to find the inference about the popul...

Q: How do you calculate a coefficient of correlation of two indexes’ returns?

A: Let the two indexes’ returns be A and B.The coefficient of correlation measures the degree to which ...

Q: Suppose x has a distribution with μ = 18 and σ = 10. (a) If a random sample of size n = 37 is drawn,...

A: In this question, it has been given that X follows a distribution with mean 18 and standard deviatio...

Q: Select the statistic test that best fits each description. Comparison of mean reading test scores by...

A: Introduction to one-way ANOVA:One-way ANOVA is a statistical method for testing hypotheses regarding...