Bus stat ch 10

An engineer has designed a valve that will regulate water pressure on an auto:

https://www.chegg.com/homework-help/questions-and-answers/engineer-designed-valve-regulate-water-pressure-automobile-engine-valve-tested-200-engines-q47461650

A newsletter publisher believes that 55% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to refute the publisher's claim?

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-55-readership-rolls-royce-sufficient-evidence-002-level-refu-q25794544

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 441 gram setting. Is there sufficient evidence at the 0.02 level that the bags are overfilled? Assume the population is normally distributed.

10.1 - 2 pic

For the given scenario, determine the type of error that was made, if any. (Hint: Begin by determining the null and alternative hypotheses.) A cell phone company claims only $50 as the mean amount its customers spend on cell phone service per month. One passionate salesperson claims that the mean amount its customers spend on cell phone service per month is less than $50. The passionate salesperson conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean amount its customers spend on cell phone service per month is $50

A cell phone company claims only $50 as the mean amount its customers spend on cell phone service per month. One passionate salesperson claims that the mean amount its customers spend on cell phone service per month is less than $50. The passionate salesperson conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean amount its customers spend on cell phone service per month is $50. Was an error made? If so, what type? Begin by writing the null and alternative hypotheses. The passionate salesperson wishes to gather data in support of the statement that the mean amount its customers spend on cell phone service per month is less than $50 Therefore, the research hypothesis is Ha: μ<50. The null hypothesis contains a strict equality, H0: μ=50 The null hypothesis is true since in reality μ=50, so the decision was to fail to reject a true null hypothesis, which is a correct decision.

One user claims that the mean number of shades the toothpaste whitens your teeth is different from four shades. The user conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean number of shades the toothpaste whitens your teeth is four shades.

No; correct decision

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.6. If the valve was designed to produce a mean pressure of 4.8 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

See 10.1 pic

A newsletter publisher believes that under 64% of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim?

Since p is the true proportion of readers who own a personal computer, the above scenario implies that for the alternative hypothesis, p is less than 0.64, and for the null hypothesis, p is equal to 0.64 Specifically, for the null hypothesis, the true proportion of readers who own a personal computer is equal to 0.64 and for the alternative hypothesis, the true proportion of readers who own a personal computer is less than 0.64. Given this information, the null and alternative hypothesis are stated below. H0: p=0.64 Ha: p<0.64

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 6.4 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications

https://www.chegg.com/homework-help/questions-and-answers/engineer-designed-valve-regulate-water-pressure-automobile-engine-valve-tested-110-engines-q39003896

A sample of 900 computer chips revealed that 31% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 34% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to dispute the company's claim?

https://www.chegg.com/homework-help/questions-and-answers/0-sample-900-computer-chips-revealed-31-chips-fail-first-1000-hours-use-company-s-promotio-q59508375

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 7.9 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 7.8 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications?

https://www.chegg.com/homework-help/questions-and-answers/engineer-designed-valve-regulate-water-pressure-automobile-engine-valve-tested-160-engines-q37123657

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 5.8 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 5.9 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve does not perform to the specifications?

https://www.chegg.com/homework-help/questions-and-answers/engineer-designed-valve-regulate-water-pressure-automobile-engine-valve-tested-290-engines-q41964745

For the given scenario, determine the type of error that was made, if any. (Hint: Begin by determining the null and alternative hypotheses.) A television network states 40% as the percentage of its viewers who are below the age of 22. One advertiser claims that the percentage of its viewers who are below the age of 22 is more than 40%. The advertiser conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the percentage of its viewers who are below the age of 22 is 45%. Was an error made? If so, what type?

https://www.chegg.com/homework-help/questions-and-answers/given-scenario-determine-type-error-made--hint-begin-determining-null-alternative-hypothes-q61163662

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 412 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled? Assume the population is normally distributed.

https://www.chegg.com/homework-help/questions-and-answers/manufacturer-chocolate-chips-would-like-know-whether-bag-filling-machine-works-correctly-4-q49108328

manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 439 gram setting. Is there sufficient evidence at the 0.02 level that the bags are underfilled or overfilled? Assume the population is normally distributed.

https://www.chegg.com/homework-help/questions-and-answers/manufacturer-chocolate-chips-would-like-know-whether-bag-filling-machine-works-correctly-4-q49803349

A sample of 1400 computer chips revealed that 54% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 57% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

https://www.chegg.com/homework-help/questions-and-answers/manufacturer-potato-chips-would-like-know-whether-bag-filling-machine-works-correctly-428--q34008367

A newsletter publisher believes that 26% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-26-readers-rolls-royce-sufficient-evidence-005-level-refute--q79624075

A newsletter publisher believes that over 50% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-50-readers-personal-computer-sufficient-evidence-005-level-s-q54696249

A newsletter publisher believes that 43% of their readers own a personal computer. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.10 level of significance, the testing firm decides to reject the null hypothesis.

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-69-readers-personal-computer-testing-firm-believes-inaccurat-q32544711

A newsletter publisher believes that less than 49% of their readers own a laptop. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.10 level of significance, the advertiser decides to reject the null hypothesis.

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-less-49-readers-laptop-marketing-purposes-potential-advertis-q30096356

A newsletter publisher believes that less than 65% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser failed to reject the null hypothesis.

https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-less-65-readers-rolls-royce-marketing-purposes-potential-adv-q76108997

A sample of 1100 computer chips revealed that 42% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 45% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim?

https://www.chegg.com/homework-help/questions-and-answers/sample-1100-computer-chips-revealed-42-chips-fail-first-1000-hours-use-company-s-promotion-q39069575

A sample of 1200 computer chips revealed that 54% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 57% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.10 level to dispute the company's claim?

https://www.chegg.com/homework-help/questions-and-answers/sample-1200-computer-chips-released-54-chips-fail-first-1000-hours-use-company-s-promotion-q39418835

A sample of 1500 computer chips revealed that 32% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 29% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim?

https://www.chegg.com/homework-help/questions-and-answers/sample-1500-computer-chips-revealed-32-chips-fail-first-1000-hours-use-company-s-promotion-q40231815

A newsletter publisher believes that 58% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm fails to reject the null hypothesis.

not sufficient

A newsletter publisher believes that 68% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to refute the publisher's claim

A newsletter publisher believes that 68% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to refute the publisher's claim? The publisher believes that 68% of the readers own a Rolls Royce. Since p is the true proportion of readers who own a Rolls Royce, the above scenario implies that for the alternative hypothesis, p is not equal to 0.68 , and for the null hypothesis, p is equal to 0.68. Specifically, for the null hypothesis, the true proportion of readers who own a Rolls Royce is equal to 0.68 and for the alternative hypothesis, the true proportion of readers who own a Rolls Royce is not equal to 0.68 . Given this information, the null and alternative hypothesis are stated below. H0: p=0.68 Ha: p≠0.68

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 445 gram setting. Is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 180 engines and the mean pressure was 6.2 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 6.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? The issue in this problem is whether or not the mean pressure of the valve is more than 6.1 lbs/sq.inch. Since μ is the true mean pressure of the new valve and the engineer wants to test if μ is more than 6.1 , this information is placed in the alternative hypothesis. Therefore, this implies that the null hypothesis states that μ is equal to 6.1. Specifically, for the null hypothesis, the true mean pressure is equal to 6.1 and for the alternative hypothesis, the true mean pressure is greater than 6.1. Given this information, the null and alternative hypothesis are stated below. H0: μ=6.1 Ha: μ>6.1

newsletter publisher believes that less than 36% of their readers own a laptop. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.01 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

As advertiser decides to reject the null hypothesis, the p-value < 0.01 This means there is sufficient evidenct at the 0.01 level of significance that the percetage is less than 36% Option A: sufficient evidence

A newsletter publisher believes that over 70% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?

Claim : A newsletter publisher believes that above 70% of their readers own a personal computer. Hypothesis test : The null and alternative hypotheses for the scenario is Ho : p = 0.70 Ha : p > 0.70

A newsletter publisher believes that 64% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.01 level of significance, the testing firm fails to reject the null hypothesis.

Correct Answer: There is not sufficient evidence at the 0.01 level of significance that the percentage is not 64

Using traditional methods it takes 104 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. After performing the test on 140 students, the researcher decides to reject the null hypothesis at a 0.05 level of significance.

Solution: Claim: new technique may lengthens training time. Null hypothesis is statement of "no significance" Alternative hypothesis is statement of "significance" So , for this example , claim is alternative hypothesis. Decision taken is "Reject the null hypothesis " at level of significance. SO , we support the alternative hypothesis. Conclusion is: THERE IS SUFFICIENT EVIDENCE

A newsletter publisher believes that over 45% of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis.

Sufficient: https://www.chegg.com/homework-help/questions-and-answers/newsletter-publisher-believes-45-readers-personal-computer-marketing-purposes-potential-ad-q67697219

For the given scenario, determine the type of error that was made, if any. (Hint: Begin by determining the null and alternative hypotheses.) A radio station has accepted 26 as the mean age of its listeners. One radio station executive claims that the mean age of its listeners is different from 26. The radio station executive conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean age of its listeners is 29. Was an error made? If so, what type?

TYPE 2

A sample of 1200 computer chips revealed that 45% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 48% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim?

The company believes that under 48% of the chips fail in the first 1000 hours of their use. Since p is the true proportion of chips which fail in the first 1000 hours, the above scenario implies that for the alternative hypothesis, p is less than 0.48, and for the null hypothesis, p is equal to 0.48 Specifically, for the null hypothesis, the true proportion of chips which fail in the first 1000 hours is equal to 0.48 and for the alternative hypothesis, the true proportion of chips which fail in the first 1000 hours is less than 0.48 . Given this information, the null and alternative hypothesis are stated below. H0: p=0.48 Ha: p<0.48

A sample of 900 computer chips revealed that 44% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that over 40% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim? State the null and alternative hypotheses for the above scenario

The null and alternative hypothesis are H0: p = 0.40 Ha: p > 0.40 This is right tailed test

A newsletter publisher believes that 55% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm fails to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

There is not sufficient evidence when failed to reject. Sufficient evidence if rejected Hawkes. You were asked to determine the conclusion, given the following scenario. A newsletter publisher believes that 55% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm fails to reject the null hypothesis. Since the testing firm wants to dispute the publisher, they want to show the proportion of customers who own a Rolls Royce is not 55% ; so this is the alternative hypothesis. Since the testing firm has failed to reject the null hypothesis, that means there is not sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, i.e. there is not sufficient evidence at the 0.05 level of significance to say that the percentage is not 55%.

A newsletter publisher believes that more than 46% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?

This is the right tailed test . The null and alternative hypothesis is H0 : p = 0.46 Ha : p > 0.46

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 401 gram setting. Is there sufficient evidence at the 0.02 level that the bags are overfilled? Assume the population is normally distributed.

Type 2: https://www.chegg.com/homework-help/questions-and-answers/given-scenario-determine-type-error-made-hint-begin-determining-null-alternative-hypothese-q56867161

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 445 gram setting. Is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.

We need to test if bags are overfilled. Hence, Our hypotheses will be: Ho: = 445 Ha: > 445

A newsletter publisher believes that 30% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis.

You were asked to determine the conclusion, given the following scenario. A newsletter publisher believes that 30% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis. Since the testing firm wants to dispute the publisher, they want to show the proportion of customers who own a Rolls Royce is not 30% ; so this is the alternative hypothesis. Since the testing firm has failed to reject the null hypothesis, that means there is not sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, i.e. there is not sufficient evidence at the 0.02 level of significance to say that the percentage is not 30%.

A newsletter publisher believes that 46% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

You were asked to determine the conclusion, given the following scenario. A newsletter publisher believes that 46% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm decides to reject the null hypothesis. Since the testing firm wants to dispute the publisher, they want to show the proportion of customers who own a Rolls Royce is not 46% ; so this is the alternative hypothesis. Since the testing firm has decided to reject the null hypothesis, that means there is sufficient evidence to support the alternative hypothesis, i.e. there is sufficient evidence at the 0.05 level of significance that the percentage is not 46%.

A sample of 1800 computer chips revealed that 52% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 55% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim?

You were asked to determine the conclusion, given the following scenario. A newsletter publisher believes that less than 52% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.10 level of significance, the advertiser failed to reject the null hypothesis. Since the advertiser wants to prove the proportion of customers who own a Rolls Royce is less than 52% , this is the alternative hypothesis. Since the advertiser has failed to reject the null hypothesis, that means there is not sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, i.e. there is not sufficient evidence at the 0.10 level of significance to say that the percentage is less than 52%.

Using traditional methods it takes 101 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 240 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.

You were asked to determine the conclusion, given the following scenario. Using traditional methods it takes 101 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 240 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance. Since the researcher believes the new technique may reduce training time, this is the alternative hypothesis. Since the researcher has failed to reject the null hypothesis, that means there is not sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, i.e. there is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Is there sufficient evidence at the 0.1 level that the bags are overfilled? Assume the population is normally distributed.

You were asked to find the null and alternative hypotheses, given the following information. A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Is there sufficient evidence at the 0.1 level that the bags are overfilled? Assume the population is normally distributed. The issue in this problem is whether or not the bags are overfilled. Since μ is the true mean filling capacity of the bags and the chocolate chips manufacturer wants to test if μ is more than 447, this information is placed in the alternative hypothesis. Therefore, this implies that the null hypothesis states that μ is equal to 447. Specifically, for the null hypothesis, the true mean filling capacity is equal to 447 and for the alternative hypothesis, the true mean filling capacity is greater than 447. Given this information, the null and alternative hypothesis are stated below. H0: μ=447 Ha: μ>447

A sample of 1400 computer chips revealed that 54% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 57% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

You were asked to find the null and alternative hypotheses, given the following information. A sample of 1400 computer chips revealed that 54% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 57% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to dispute the company's claim? The company believes that 57% of the chips fail in the first 1000 hours of their use. Since p is the true proportion of chips which fail in the first 1000 hours, the above scenario implies that for the alternative hypothesis, p is not equal to 0.57, and for the null hypothesis, p is equal to 0.57 Specifically, for the null hypothesis, the true proportion of chips which fail in the first 1000 hours is equal to 0.57 and for the alternative hypothesis, the true proportion of chips which fail in the first 1000 hours is not equal to 0.57 Given this information, the null and alternative hypothesis are stated below. H0: p=0.57 Ha: p≠0.57

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 5.4 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 5.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs below the specifications?

You were asked to find the null and alternative hypotheses, given the following information. An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 5.4 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 5.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs below the specifications? The issue in this problem is whether or not the mean pressure of the valve is less than 5.6 lbs/sq.inch. Since μ is the true mean pressure of the new valve and the engineer wants to test if μ is less than 5.6 , this information is placed in the alternative hypothesis. Therefore, this implies that the null hypothesis states that μ is equal to 5.6. Specifically, for the null hypothesis, the true mean pressure is equal to 5.6 and for the alternative hypothesis, the true mean pressure is less than 5.6 . Given this information, the null and alternative hypothesis are stated below. H0: μ=5.6 Ha: μ<5.6

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 6.7 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications?

You were asked to find the null and alternative hypotheses, given the following information. An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 6.7 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications? The issue in this problem is whether or not the mean pressure of the valve is less than 6.7 lbs/sq.inch. Since μ is the true mean pressure of the new valve and the engineer wants to test if μ is less than 6.7 , this information is placed in the alternative hypothesis. Therefore, this implies that the null hypothesis states that μ is equal to 6.7 Specifically, for the null hypothesis, the true mean pressure is equal to 6.7 and for the alternative hypothesis, the true mean pressure is less than 6.7. Given this information, the null and alternative hypothesis are stated below.