Historically, the earnings of mechanical engineers, graduates of any university, have followed anormal distribution with a standard deviation of $300, have followed a normal distribution witha standard deviation of $300. In a certain study, a random sample of 25 engineers a randomsample of 25 engineers from EPN and an independent sample of 30 engineers from ESPE weretaken. From the results of the sample, it was observed that the average income of the EPNengineers was $1,000 with a standard deviation of $275; and that the ESPE engineers had anaverage income of $1,300 and a standard deviation of $350.a) At a 98% confidence level, is it reasonable to assume that the standard deviations of theearnings of EPN and ESPE engineers are equal? are the earnings of EPN and ESPE engineersequal?b) With a 90% confidence level, is it reasonable to say that the average income of EPNengineers is lower than that of ESPE engineers? EPN engineers is lower than that of ESPEengineers?

Answered: Historically, the earnings of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a research study, conducted by the National Institute of Health, 25 individuals were sampled measuring their triglyceride levels. If the distribution of triglyceride levels for 25 to 55 year old females has a mean of 211 mg/dl and a standard deviation of 46 mg/dl, what is the probability that our sample mean will be above 240?
A personal trainer states that the distribution of running times (in seconds) for a 100-meter dash is normally distributed with a mean of 0.12 seconds and a standard deviation equal to 0.04 seconds. She wishes to improve running time by incorporating a set of breathing exercises into the daily workout. She randomly assigns some players to the new regimen in order to compare them to players who continue to follow the old workout. After six weeks, she records the average running time of the two groups of players. a. In the original distribution, what percentage of the players on the team run the 100-meter dash faster than 0.16 seconds? b. Define the independent and dependent variables. c. The personal trainer believes that the new breathing exercises have a significant improvement on running times. State the null and alternative hypotheses.
Some battery manufacturers claim that the average battery life of the company is 240 hours. There is a theory in the quality department of the company that the lifespan is different from 240 hours. The Quality Department therefore decided to conduct an experiment to test this theory. A random sample of size 18 was taken and the lifespan was examined. The average life of the batteries examined was 237,056 hours and the standard deviation was 11,280. Battery life can be expected to follow a normal distribution.a) Find a 95% confidence interval for the average battery life.b) Examine with an appropriate hypothesis test whether the average battery life differs from 240 hours.sometimes. Use α = 0.05.
Suppose that El Camino is studying the average number of hours students study for classes per week. According to research from 2010 El Camino students spent an average of 21 hours a week studying for classes. El Camino wants to study if this average has changed. To do this they take a random sample of 81 current students and find that the average student spent 19.3 hours studying with a standard deviation of 6.4 hours. (Note: You may assume there are approximately 20,000 El Camino students). (a) Carry out a hypothesis test at α = .05 to test the claim that the average number of hours per week that El Camino students study has changed since 2010. (b) Describe what it would mean in this situation to make a Type I error (c) Describe what it would mean in this situation to make a Type II error (d) Construct a 95% confidence interval for the average number of hours studied by El Camino students per week. Make sure to interpret your interval.
What would be the correct way of doing this?
A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 198 with a standard deviation of 43. A random sample of 110 adults was chosen. What is the probability that the mean cholesterol level is between 193 and 202?
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Scientists collect a simple random sample of 25 menthol cigarettes and 25 non-menthol cigarettes. Both samples consist of cigarettes that are filtered, 100mm long, and non-light. The menthol cigarettes have a mean nicotine amount of 0.87 mg and a standard deviation of 0.24 mg. The non-menthol cigarettes have a mean nicotine amount of 0.92 mg and a standard deviation of 0.25 mg. Use a 0.05 significance level to test the claim that non-menthol cigarettes have greater amounts of nicotine than menthol cigarettes. Assume population variances are not equal.
A nurse is interested in the amount of time patients spend exercising per day. According to a recent study, the daily workout time per adult follows an approximately normal distribution with a mean of 94 minutes and a standard deviation of 27minutes. If the nurse randomly samples patients in her office to analyze their exercise time and gets a standard error of 3minutes, how many patients did she sample?
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players' salaries and 35 football players' salaries is selected. The mean salary is determined for both samples. Let -, represent the difference in the mean salaries for baseball and football players. Which of the following represents the shape of the sampling distribution for ,-7,? skewed right since the populations are both right skewed skewed right since the differences in salaries cannot be negative approximately Normal since both sample sizes are greater than 30 approximately Normal since the sum of the sample sizes is greater than 30
According to the Insurance Association in US, the average annual expenditure for automobile insurance is $605. Suppose that in a simple random sample of 80 residents of New York, for most recent year their average expenditure was $638.62 with the standard deviation of $106.05. Based on these data, examine whether the average annual insurance for motorists in New York might be different from that in national level. Using the 0.05 level of significance, what conclusion do you reach? Also, construct and interpret 95% confidence interval for the population mean. Is the hypothesized mean within the interval? Is this consistent with the findings of the hypothesis test conducted?
a Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was 9 months (3/4 year) with a standard deviation of 2 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old. Conduct a hypothesis test at the 5% level. a. What is the p-value? (Round your answer to four decimal places.) b. What is the test statistic

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