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 0.7. If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.
Added by Pilar R.
Close
Step 1
The first step is to state the null hypothesis and the alternative hypothesis. Null hypothesis: μ = 4.7 (The valve performs as per the specifications) Alternative hypothesis: μ > 4.7 (The valve performs above the specifications) Show more…
Show all steps
Your feedback will help us improve your experience
T. L. and 83 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines and the mean pressure was 5.8 lbs/square inch. Assume the standard deviation is known to be 0.6. If the valve was designed to produce a mean pressure of 5.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?
Chris M.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.9 . If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.
Danielle F.
Down the toilet A company that makes hotel toilets claims that its new pressure-assisted toilet reduces the average amount of water used by more than 0.5 gallon per flush when compared to its current model. To test this claim, the company randomly selects 30 toilets of each type and measures the amount of water that is used when each toilet is flushed once. For the current-model toilets, the mean amount of water used is 1.64 gal with a standard deviation of 0.29 gal. For the new toilets, the mean amount of water used is 1.09 gal with a standard deviation of 0.18 gal. (a) Carry out an appropriate significance test. What conclusion would you draw? (Note that the null hypothesis is not $H_{0} : \mu_{1}-\mu_{2}=0$ ) (b) Based on your conclusion in part (a), could you have made a Type I error or a Type II error? Justify your answer.
Comparing Two Populations or Groups
Comparing Two Means
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD