Quiz IV Practice - Introduction to Statistics | MATH 1121 | Quizzes Statistics

Math 1121 Quiz 4 Practice

1. What would be the test statistic, z, to test the claim

172 1. , given a sample of size n

49 for

which x

170 2. ? Assume that

46 6. .

For each hypothesis test please provide the following information:

(a) State the null and the alternate hypotheses.

(b) Identify the sampling distribution to be used: the standard normal distribution or the

student’s t distribution.

(d) Based on your answers to parts (a) through (c) decide whether to reject or not reject the null

hypothesis at the given significance level. Explain your conclusion in simple non-technical

terms.

2. Some professional football players seem to earn tremendous amounts of money. However,

their careers as professional players are short. One sports magazine reported that the average

career length is 4.3 years. A random sample of 40 retired players showed a sample mean career

length of 5.2 years with standard deviation 2.3 years. Construct a hypothesis test to determine

whether the average career in professional football is longer than 4.3 years. Use a 5% level of

significance.

3. Statistical Abstracts (117th edition) reports that the average annual expenditure for health care

by individuals 25 to 34 years old is $1,096. A random sample of 24 athletes between the ages of

25 and 34 had a sample mean expenditure of $950 with sample standard deviation $425. Test to

see if the mean expenditure for health care for athletes between the ages of 25 and 34 is different

from the national average. Use a 1% significance level.

4. According to Statistical Abstracts (117th edition) 27% of the adults in the United States visited

an art museum at least once last year. A random sample of 200 residents of a large city showed

that 80 of them had visited an art museum during the past year. Test to see if the proportion of

people in this area who visit art museums is higher than the national average. Find the P value

for your test statistic and use it to determine if the data is statistically significant. Use a 5%

significance level.

5. Statistical Abstracts (117th edition) gives wheat production figures (in bushels per acre) for

1994 and 1996 for leading wheat producing states. A random sample of

8 states produced the following data. The same states were used for both years.

(a) Is this a case of paired data or independent random samples?

(b) Test to see if there is a difference in population mean wheat production for 1994 and 1996.

Use a 5% significance level.

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Math 1121 Quiz 4 Practice

1. What would be the test statistic, z , to test the claim μ = 172 1. , given a sample of size n = 49 for

which x = 170 2.? Assume that σ = 46 6..

For each hypothesis test please provide the following information: (a) State the null and the alternate hypotheses. (b) Identify the sampling distribution to be used: the standard normal distribution or the student’s t distribution. (c) Find the P value for the sample test statistic. (d) Based on your answers to parts (a) through (c) decide whether to reject or not reject the null hypothesis at the given significance level. Explain your conclusion in simple non-technical terms.

Some professional football players seem to earn tremendous amounts of money. However, their careers as professional players are short. One sports magazine reported that the average career length is 4.3 years. A random sample of 40 retired players showed a sample mean career length of 5.2 years with standard deviation 2.3 years. Construct a hypothesis test to determine whether the average career in professional football is longer than 4.3 years. Use a 5% level of significance.
Statistical Abstracts (117th edition) reports that the average annual expenditure for health care by individuals 25 to 34 years old is $1,096. A random sample of 24 athletes between the ages of 25 and 34 had a sample mean expenditure of $950 with sample standard deviation $425. Test to see if the mean expenditure for health care for athletes between the ages of 25 and 34 is different from the national average. Use a 1% significance level.
According to Statistical Abstracts (117th edition) 27% of the adults in the United States visited an art museum at least once last year. A random sample of 200 residents of a large city showed that 80 of them had visited an art museum during the past year. Test to see if the proportion of people in this area who visit art museums is higher than the national average. Find the P value for your test statistic and use it to determine if the data is statistically significant. Use a 5% significance level.
Statistical Abstracts (117th edition) gives wheat production figures (in bushels per acre) for 1994 and 1996 for leading wheat producing states. A random sample of 8 states produced the following data. The same states were used for both years.

(a) Is this a case of paired data or independent random samples? (b) Test to see if there is a difference in population mean wheat production for 1994 and 1996. Use a 5% significance level.

How long do RN’s work in the nursing field? The answer might vary depending on the age of the nurse when he or she obtained the RN degree. A random sample of 80 retired nurses who received their RN’s before age thirty was surveyed. The mean length of time they worked as an RN was 9.7 years with standard deviation 2.8 years. An independent random sample of 70 retired nurses who received their RN degrees at age thirty or later indicated that their mean length of service in the profession was 10.2 years with standard deviation 2.4 years. Test to see if the nurses who get their RN degrees later in life stay in the profession longer. Use a 1% significance level.
Does it make a difference which word-processing software you use? A random sample of 25 experienced secretaries were given the task of typing, proofreading and formatting a fifty-page document. Thirteen used Word Master software while the rest used Super Word software. The mean time required to produce the document using Word Master was 12.6 hr with standard deviation 1.7 hr. The mean time for the group using Super Word was 13.3 hr with standard deviation 1.9 hr. Test the claim that there is no difference in the mean time using the two packages. Use a 1% level of significance.
Have eating habits changed? In 1990 a random sample of 100 people surveyed showed that 39 ate red meat twice a week or less. In 1996 an independent random sample of 80 people showed 36 ate red meat twice a week or less. In this time period has the proportion of people limiting their consumption of red meat changed? Use a 5% significance level.
Walter Gleason is an astronomer who has been studying radio signals from the planet Jupiter. Over a long period of time, the planet’s electromagnetic field has been sending low-frequency signals with a mean frequency of 14.2 megahertz. A recent space module that went by Jupiter recorded a major volcanic eruption that may have covered a large surface on the planet. For the past several months Walter has been measuring Jupiter’s radio signals of a random time schedule. A group of 75 measurements gave a mean 14.49 megahertz with sample standard deviation 0.9 megahertz. Test to see if the mean radio frequency of these signals has changed. Calculate the P value for your test statistic and determine if this data is statistically significant. Use a 1% significance level.
The Dog Days Lawn Service advertises that it will completely maintain your lawn at an average cost per customer of $55 per month. A random sample of 18 Dog Days customers had a sample mean cost of $59.50 with sample standard deviation $10.50. Do the data support the claim that the average cost is more than $55? Use a 5% significance level.

Reference: [9.52]

[7] H 0 : μ 1 = μ 2 ; H 1 :μ 1 ≠ μ 2 ; t 0 = ± 2 .807; P value is 0.34. Do not reject H 0. We cannot

conclude that there is any difference in the mean word-processing time.

Reference: [9.70] [8] (^) H (^) 0 : p 1 (^) = p 2 (^) ; H (^) 1 : p 1 (^) ≠ p 2 ; P value = 0.417; Do not reject (^) H 0 .We cannot conclude that the

number of people limiting their consumption of red meat has changed.

Reference: [9.79]

[9] H 0 : μ = 14.2; H 1 : μ ≠ 14.2; P value: 0.0052; Reject H 0. The mean radio frequency has

changed. The data is statistically significant at the 1% significance level.

Reference: [9.46] [10] PH0: μ = $55; H1: μ > $55. P value is .0433. Reject (^) H 0. The mean cost for the lawn

service is greater than $55.

Quiz IV Practice - Introduction to Statistics | MATH 1121, Quizzes of Statistics

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