STEP BY STEP Critical Value Approach to Hypothesis Testing 1- State H o and H 1 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 H o If the test statistics falls into rejection region, REJECT H o The managerial conclusion is written in the context of the real world problem.

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 ClassFreq Total: 50 MfMfM 2 _______

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 36 pairs of shoes from a catalog and finds the following costs. Is there enough evidence to support the researcher`s claim at α = Assume σ= ∑x =2700

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 with a standard deviation of 2 years. Is there evidence to support the claim at α = 0.05? Use p-value method.

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.

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 sample is 0.6 mile per hour. At α = 0.05, is there enough evidence to reject the claim? Use p-value method.

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?

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.

CORRECT DECISION 1-α TYPE II ERROR ( β ERROR) TYPE I ERROR (α ERROR) CORRECT DECISION 1-β DO NOT REJECT H 0 REJECT H 0 H 0 IS FALSE H 0 IS TRUE 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. ACTUAL SITUATION STATISTICAL DECISION

Exercise - 1 One Tailed Test TEST at the 5% level whether the single sample value of 172 comes from a normal population with mean µ= 150 and variance σ 2 =100.

Exercise –McDonald One Tailed Test In one past study, McDonald’s had a mean service time of seconds. Suppose that this company began a quality improvement effort to reduce the service time and selected a sample of 25 stores. The sample mean has been calculated as seconds and sample standard deviation is 20.2 seconds. You wish to determine whether the new drive-through process has a mean that is less than seconds.

Exercise - 2 One Tailed Test TEST at the 1% level whether the single sample value 54 has been drawn from a normal population with mean 65 and variance 30 or whether the mean is less than 65.

Exercise – 3 The manager of the women`s dress department of a department store wants to know whether the true average number of women`s dresses sold per day is 24. If in a random sample of 36 days the average number of dresses sold is 23 with a standard deviation of 7 dresses, Is there, at the 0.05 level of significance, sufficient evidence to reject the null hypothesis that µ=24?

Exercise – 4

Exercise – 5

Exercise – 6

Exercise – 7