# One population mean

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## A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. the mean score

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Question: a study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. the mean score on the final exam for a course using the old edition is 75. ten randomly selected people who used the new text take the final exam their scores are shown.
person: A,B,C,D,E,F,G,H,I,J
score: 90,74,96,95,89,71,80,86,67,78
Use a 0.01significance level to test the claim that people do better with the new edition. Assume the standard deviation is 10.5. ( Note you may wish to use statistical software).
A.)what kind of test should be used?
1. two-sided tail
2. one tailed
3. it does not matter
B.) the test statistic is (rounded to two decimals)
C.) the P-value is
D.) is there sufficient evidence to support the claim that people do better than 75 on this exam? Y/N
E.) construct a 99% confidence interval for the mean score for students using the new text. ____<mean<____

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## Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes. The franchise has installed

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Question : Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

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## A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma

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Question :  Hypothesis Testing

A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma was $520. Suppose you would like to determine if the average weekly pay for all working women is significantly greater than that for women with a high school diploma. Data providing the weekly pay for a sample of 50 working women are available in the Excel file (Weekly Pay). Formulate the null and alternative hypotheses and conduct the appropriate test. What is your conclusion? Weekly Pay 582 320 290 542 678 596 760 565 772 333 685 800 619 697 557 804 687 691 759 599 696 950 750 657 675 498 633 753 627 614 569 617 736 712 629 553 679 548 679 1230 565 533 523 641 667 570 598 648 587 424 • Sale! ## Congress regulates corporate fuel economy and sets an annual gas mileage for cars.$3.00 $2.00 Question: Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to meet the goal of 30.4 mpg or better for their fleet of cars. To see if the goal is being​met, they check the gasoline usage for 46 company trips chosen at ​random, finding a mean of 31.4 mpg and a standard deviation of 2.57 mpg. Is this strong evidence that they have attained their fuel economy​ goal? Use 0.05 as the​ level of significance. p-Value = 0.006. State an appropriate conclusion. Choose the correct answer below. • Sale! ## A random sample of size 12 from a normal population is given below. 69 74 75 76 78 79 81 83 83 85 86 87$2.00 $1.00 Question: A random sample of size 12 from a normal population is given below. 69 74 75 76 78 79 81 83 83 85 86 87 a) Someone claimed that s = 10. Does this data set support the claim? Test at a = 0.05. b) Test if the population mean is 85 using a = 0.05. c) Find the p-value of the test • Sale! ## Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes$2.00 $1.00 Question: Last month the waiting time at the drive-through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion? • Sale! ## The life in hours of an electronic sensor is known to be approximately Normally distributed$3.00 \$2.00

Question:

The life in hours of an electronic sensor is known to be approximately Normally distributed, with population standard deviation  = $\sigma&space;=&space;20$ hours. A random sample of 10 sensors resulted in the following data: 500,550,560,575,525,505,510,540,550,545.

• Is there evidence to support the claim that mean life exceeds 520 hours? Use a fixed-level test with alpha = 0.05.
• What is the P-value of this test? Conclude the same of part (a)?
• What is the Beta-value for this test if the true mean life is 535 hours?
• What sample size would be required to ensure that Beta does not exceed 0.10 if the true mean life is 540 hours?
• Construct a 95% one-sided lower CI on the mean life.
• Use the CI found in part e) to test the hypothesis.