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A group of statistics students decided to conduct a survey at theiruniversity to find the average (mean) amount of time students spendstudying per week. Based on a simple random sample, they surveyed144 students. The statistics showed that the student populationstudied an average of 20 hours per week with a standard deviationof 10 hours.
(a) What is the standard error of the mean?

(b) What is the probability that a sample mean would exceed 20hours per week?

(c) What is the probability of finding a sample mean less than 18hours?

(d) What is the probability that average student study time isbetween 18 and 22 hours?

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Retselisitsoe Pokothoane
Retselisitsoe PokothoaneLv10
28 Sep 2019

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Related questions

(15.28) Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.4. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 24.

In answering the following, use z-scores rounded to two decimal places.

If you choose one student at random, what is the probability (±±0.0001) that the student's score is between 20 and 30?

You sample 22 students. What is the standard deviation (±±0.01) of the sampling distribution of their average score x¯¯¯x¯?

What is the probability (±±0.0001) that the mean score of your sample is between 20 and 30?

1. A researcher believes that the average size of farms in the U.S. has increased from the 2002 mean of 471 acres. She took a sample of 23 farms in 2011 to test her belief and found a sample mean of 487 acres and a sample standard deviation of 46.9 acres. At a 5% level of significance, test the researcher's claim. What is your conclusion?

2. A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 410 accounting firms and determines that 304 of these firms have flexible scheduling. At a 1% level of significance, does your test show enough evidence to conclude that a significantly lower percentage of accounting firms offer employees flexible scheduling? What is the p-value for this test?

3. The American Lighting Company developed a new light bulb that it believes will last at least 700 hours on average. A test is to be conducted using a random sample of 50 bulbs, and a 1% level of significance. Assume that the population standard deviation is 10 hours. What are the consequences of making a type II error? What is the probability of making a Type II error if the true population mean is 695 hours?

An employee survey conducted two years ago Packard Motors Inc. found

benets compared to the survey two years ago.

a) What is the standard error of the sample proportion who are concerned?

b)What is the probability that the sample proportion is less than 0.5?

c)What is the upper limit of the sample proportion such that only 3%of the time the sample proportion would exceed this value


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