Question

1. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 150 engines and the mean pressure was 4.3 pounds/square inch. Assume the standard deviation is known to be 0.8. A level of significance of 0.05 will be used. Determine the decision rule.

Enter the decision rule.

2. A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 20 is made, and it is found that they have a mean of 2047.0 millimeters with a standard deviation of 30.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

3. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 8.1 pounds/square inch with a variance of 0.25. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

4. A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 413.0 gram setting. It is believed that the machine is underfilling the bags. A 33 bag sample had a mean of 406.0 grams. A level of significance of 0.02 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the variance is known to be 256.00.

What is the conclusion?

A. There is not sufficient evidence to support the claim that the bags are undefilled.

B. There is sufficient evidence to support the claim that the bags are underfilled.

5.

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404.0 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 400.0 grams. A level of significance of 0.05 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the standard deviation is known to be 26.0.

What is the conclusion?

A. There is not sufficient evidence to support the claim that the bags are undefilled.

B. There is sufficient evidence to support the claim that the bags are underfilled.

Answer 1

1). hypothesis:-

where is the mean water pressure on an automobile engine.

this is a right tailed test.

as the population sd is known we will do 1 sample z test for mean.

given data are:-

sample mean () = 4.3

population sd () = 0.8

sample size (n)= 150

z critical value at 95% confidence level is = 1.645 (as this is one tailed test)

the decision rule be:-

reject the null hypothesis if,

test statistic be:-

decision:-

so, we fail to reject the null hypothesis.

we conclude that,

there is not sufficient evidence to  believe that the valve performs above the specifications.

2).given data are:-

sample mean () = 2047

sample sd (s) = 30

sample size (n)= 20

hypothesized mean () = 2058

as the sample sd is given , we will perform 1 sample t test for mean.

test statistic be:-

3).hypothesis:-

where is  mean water pressure on an automobile engine

given data are:-

sample mean () = 8.1

sample sd (s) = = 0.5

sample size (n)= 24

hypothesized mean () = 7.9

as the sample sd is given , we will perform 1 sample t test for mean.

test statistic be:-

degrees of freedom = (n-1) = (24-1) = 23

t critical value for df = 23 , alpha= 0.10, right tailed test be:-

[using t distribution table]

decision:-

so, we reject the null hypothesis.

4).hypothesis:-

where is the mean weight of bags in grams

this is a left tailed test.

as the population sd is known we will do 1 sample z test for mean.

given data are:-

sample mean () = 406

population sd () = =16

sample size (n)= 33

z critical value at 98% confidence level is = -2.05 (as this is left tailed test)

test statistic be:-

decision:-

so, we reject the null hypothesis.

we conclude that,

There is sufficient evidence to support the claim that the bags are underfilled.

5).hypothesis:-

where is the mean weight of bags in grams

this is a left tailed test.

as the population sd is known we will do 1 sample z test for mean.

given data are:-

sample mean () = 400

population sd () =26

sample size (n)= 39

z critical value at 95% confidence level is = -1.96 (as this is left tailed test)

test statistic be:-

decision:-

so, we fail to reject the null hypothesis.

we conclude that,

There is not sufficient evidence to support the claim that the bags are underfilled.

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