1. Exercise - 1
A package-filling process at a Cement company fills bags of cement to an average weight of µ but µ changes from time to time. The standard deviation is σ = 3 pounds. A sample of 25 bags has been taken and their mean was found to be 150 pounds.
Assume that the weights of the bags are normally distributed.
Find the 90% confidence limits for µ.

3. Exercise - 3
An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000.
What is the upper end point in a 99% confidence interval for the average income?

4. Exercise - 4
An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000.
What is the width of the 90% confidence interval?

7. STEP BY STEP
Critical Value Approach to Hypothesis Testing
1- State Ho and H1
2- Choose level of significance, α
Choose the sample size, n
3- Determine the appropriate test statistics and sampling distribution.
4- Determine the critical values that divide the rejection and non-rejection areas.
5- Collect the sample data, organize the results and compute the value of the test
statistics.
6- Make the statistical decision and state the managerial conclusion
If the test statistics falls into non-rejection region, DO NOT REJECT Ho
If the test statistics falls into rejection region, REJECT Ho
The managerial conclusion is written in the context of the real world problem.

8. Exercise –Hourly wage
The president of a company states that the average hourly wage of his/her employees is 8.65 TRL. A sample of 50 employees has the distribution shown below. At α=0.05, is the president’s statement believable? Assume σ=0.105 TRL
M fM fM2 _______
Class Freq.
Total:

9. Exercise – Athletic Shoes
A researcher claims that the average cost of men`s athletic shoes is less than 80 USD. He selects a random sample of 35 pairs of shoes from a catalog and finds the following costs. Is there enough evidence to support the researcher`s claim at α = 0.10. 60 70 75 55 80 50 40 95
120 90 85
110 65 45
∑x =2630
∑(x−x̄)²= 12824

10. Exercise –INFECTIONS
A medical investigation claim that the average number infections per week at a hospital is A random sample of 10 weeks had a mean number of 17.7 infections. The sample standard deviation is 1.8
Is there evidence to reject the investigator’s claim at α = 0.05?
Assume the variable is normally distributed .

11. Exercise –Internet Access Z-test for Proportion
Of 2000 adults, 1540 said that they wanted Internet Access so, they could check personal while on vacation. A survey conducted in the previous year indicated that 75% of adults wanted Internet Access.
Is there evidence that the percentage of adults who wanted Internet Access has changed from the previous year

12. Exercise – Life Guards
A researcher wishes to test the claim that the average age of lifeguards in a city is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7 years. Population standard deviation is assumed to be 2 years. Is there evidence to support the claim at α = 0.05?
Use p-value method.

13. Exercise – Assist. Prof.
A researcher reports that the average salary of assistant professors is more than 42,000 TL. A sample of 30 assistant professors has a mean salary of 43,260 TL. At α = 0.05, Test the claim that assistant professors earn more than 42,000 TL a year. The population standard deviation is 5,230 TL.

14. Exercise – Wind Speed
A researcher claims that the average wind speed in a certain city 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the population is 0.6 mile per hour. At α = 0.05, is there enough evidence to reject the claim?
Use p-value method.

15. Exercise – Starting Salary
A job placement director claims that the average starting salary for nurses is 24,000 USD. A sample of 10 nurses` salaries has a mean of 23,450 USD and a standard deviation of 400 USD. Is there enough evidence to reject the director`s claim at α=0.05?

16. Exercise – Attorney Advertisements
An attorney claims that more than 25% of all lawyers advertise. A sample of 200 lawyers in a certain city showed that 63 had used some form of advertising.
At α = 0.05, is there enough evidence to support the attorney`s claim?
Use the p-value method.

17. Exercise – Sugar
Sugar is packed in 5 kg bags. An inspector suspects the bags may not contain 5 kg. A sample of 50 bags produces a mean of 4.6 kg and a standard deviation of 0.7 kg.
Is there enough evidence to conclude that the bags do not contain 5 kg as stated at α = 0.05?
Also find the 95% CI of the true mean.

18. A researcher thinks that if expectant mother use vitamin pills, the birth weight of the babies will increase . The average birth weight of the population is 3.5 kg.
H0:µ = 3.5 and H1 : µ > 3.5

19. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 18.
H0:µ = 18 and H1 : µ < 18

20. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73.
H0:µ = 73 and H1 : µ ≠ 73

21. CORRECT DECISION TYPE I ERROR (α ERROR) TYPE II ERROR (β ERROR)
ACCEPT H0
REJECT H0
CORRECT DECISION
TYPE I ERROR
(α ERROR)
TYPE II ERROR
(β ERROR)
H0 IS TRUE
H0 IS FALSE
If the null hypothesis is true and accepted or false and rejected the decision is in either case CORRECT.
If the null hypothesis is true and rejected or false and accepted the decision is in either case in ERROR.

22. Example : Fast-Food Restaurant
You are manager of a fast-food restaurant. You want to determine whether the waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes.
A-) State the null Hypothesis and Alternative Hypothesis
From past experience, you can assume that the population is normally distributed with the standard deviation of 1.2 minutes. You select a sample of 30 orders during one-hour period. The sample mean is 5.1 minutes.
B- Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes.
C- Find and use p-Value approach to test the Hypothesis.