
a. To state:
The null and alternative hypothesis.

Answer to Problem 18E
Solution:
The null hypothesis is
Explanation of Solution
Consider the following scenario,
“Teachers’ salaries in one state are very low, so low that educators in that state regularly complain about their compensation. The state mean is $33, 600, but teachers in one district claim that the mean in their district is significantly lower. They survey a simple random sample of 22 teachers in the district and calculate a mean salary of $32, 400 with a standard deviation of $1520”.
State the null and alternative hypothesis.
Suppose teachers claims that mean in their district is significantly lower than state mean of $33, 600. That is the research hypothesis mathematically as
The Null hypothesis:
The alternative hypothesis:
Final statement:
The null hypothesis is
b. To determine:
Which distribution to use for the test statistic, and state the level of significance.

Answer to Problem 18E
Solution:
The t-test statistic is used and the level of significance of
Explanation of Solution
The t-test statistic is appropriate to use in this case because the claim is about a population mean, the populations
So, t-test statistic is used and the level of significance of
Final statement:
The t-test statistic is used and the level of significance of
c. To gather:
The data and calculate the necessary sample statistics.

Answer to Problem 18E
Solution:
The calculated test statistic is -3.7030.
Explanation of Solution
The test statistic formula:
Test statistic for a hypothesis test for a population mean (
When the population standard deviation is unknown, the sample taken is a simple random sample, and either the
Where n is the sample size,
The given information is,
Substitute these values in the test statistic formula to get the following,
So, the calculated test statistic is -3.7030.
Final statement:
The calculated test statistic is -3.7030.
d. To draw:
To Draw a conclusion and interpret the decision.

Answer to Problem 18E
Solution:
There is a significance evidence to support the teachers’ claims that the mean in their district is significantly lower at the 0.01 level of significance.
Explanation of Solution
Assume that the population standard deviation is unknown and the population distribution is approximately normal.
Rejection Region for Hypothesis Tests for Population Means (
If p-value
If p- value
Degrees of Freedom for t in a Hypothesis Test for a Population Means (
In a hypothesis test for a population mean where the population standard deviation is unknown, the number of degrees of freedom for the Student’s t- distribution of the test statistic is given by
Where n is the sample size.
Form the given information this is the left-tailed test since
From the given information n = 22 then the degrees of freedom is given below,
Conclusion:
Consider the level of significance of
Use the “p value of t-test statistic” calculator to get the following,
The p -value is approximately 0.0007. Since
The diagrammatic representation is given below,
Thus the conclusion is to reject the null hypothesis.
So, there is significance evidence to support the teachers’ claims that the mean in their district is significantly lower at the 0.01 level of significance.
Final statement:
There is a significance evidence to support the teachers’ claims that the mean in their district is significantly lower at the 0.01 level of significance.
Want to see more full solutions like this?
Chapter 10 Solutions
Beginning Statistics, 2nd Edition
- Suppose we wish to test the hypothesis that women with a sister’s history of breast cancer are at higher risk of developing breast cancer themselves. Suppose we assume that the prevalence rate of breast cancer is 3% among 60- to 64-year-old U.S. women, whereas it is 5% among women with a sister history. We propose to interview 400 women 40 to 64 years of age with a sister history of the disease. What is the power of such a study assuming that the level of significance is 10%? I only need help writing the null and alternative hypotheses.arrow_forward4.96 The breaking strengths for 1-foot-square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,250 pounds per square inch (psi) and a standard deviation of 10.2 psi. Find the probability of selecting a 1-foot-square sample of material at random that on testing would have a breaking strength in excess of 2,265 psi.4.97 Refer to Exercise 4.96. Suppose that a new synthetic fabric has been developed that may have a different mean breaking strength. A random sample of 15 1-foot sections is obtained, and each section is tested for breaking strength. If we assume that the population standard deviation for the new fabric is identical to that for the old fabric, describe the sampling distribution forybased on random samples of 15 1-foot sections of new fabricarrow_forwardUne Entreprise œuvrant dans le domaine du multividéo donne l'opportunité à ses programmeurs-analystes d'évaluer la performance des cadres supérieurs. Voici les résultats obtenues (sur une échelle de 10 à 50) où 50 représentent une excellente performance. 10 programmeurs furent sélectionnés au hazard pour évaluer deux cadres. Un rapport Excel est également fourni. Programmeurs Cadre A Cadre B 1 34 36 2 32 34 3 18 19 33 38 19 21 21 23 7 35 34 8 20 20 9 34 34 10 36 34 Test d'égalité des espérances: observations pairéesarrow_forward
- A television news channel samples 25 gas stations from its local area and uses the results to estimate the average gas price for the state. What’s wrong with its margin of error?arrow_forwardYou’re fed up with keeping Fido locked inside, so you conduct a mail survey to find out people’s opinions on the new dog barking ordinance in a certain city. Of the 10,000 people who receive surveys, 1,000 respond, and only 80 are in favor of it. You calculate the margin of error to be 1.2 percent. Explain why this reported margin of error is misleading.arrow_forwardYou find out that the dietary scale you use each day is off by a factor of 2 ounces (over — at least that’s what you say!). The margin of error for your scale was plus or minus 0.5 ounces before you found this out. What’s the margin of error now?arrow_forward
- Suppose that Sue and Bill each make a confidence interval out of the same data set, but Sue wants a confidence level of 80 percent compared to Bill’s 90 percent. How do their margins of error compare?arrow_forwardSuppose that you conduct a study twice, and the second time you use four times as many people as you did the first time. How does the change affect your margin of error? (Assume the other components remain constant.)arrow_forwardOut of a sample of 200 babysitters, 70 percent are girls, and 30 percent are guys. What’s the margin of error for the percentage of female babysitters? Assume 95 percent confidence.What’s the margin of error for the percentage of male babysitters? Assume 95 percent confidence.arrow_forward
- You sample 100 fish in Pond A at the fish hatchery and find that they average 5.5 inches with a standard deviation of 1 inch. Your sample of 100 fish from Pond B has the same mean, but the standard deviation is 2 inches. How do the margins of error compare? (Assume the confidence levels are the same.)arrow_forwardA survey of 1,000 dental patients produces 450 people who floss their teeth adequately. What’s the margin of error for this result? Assume 90 percent confidence.arrow_forwardThe annual aggregate claim amount of an insurer follows a compound Poisson distribution with parameter 1,000. Individual claim amounts follow a Gamma distribution with shape parameter a = 750 and rate parameter λ = 0.25. 1. Generate 20,000 simulated aggregate claim values for the insurer, using a random number generator seed of 955.Display the first five simulated claim values in your answer script using the R function head(). 2. Plot the empirical density function of the simulated aggregate claim values from Question 1, setting the x-axis range from 2,600,000 to 3,300,000 and the y-axis range from 0 to 0.0000045. 3. Suggest a suitable distribution, including its parameters, that approximates the simulated aggregate claim values from Question 1. 4. Generate 20,000 values from your suggested distribution in Question 3 using a random number generator seed of 955. Use the R function head() to display the first five generated values in your answer script. 5. Plot the empirical density…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





