Scenario: During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.)
2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80
2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45
Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level.
Let us go through the steps:
The first step in hypothesis testing is to specify the null hypothesis (Ho) and the alternative hypothesis (Ha)
Ho: The average game is 3.5 hours (u=3.5)
Ha: The average game is less then 3.5 hours (u<3.5)
The next step is to select a significance level. Typically the 0.05 as stated in the question.
Next we calculate the test statistic:
The formula would be: the average of our sample (x) - the average stated (x bar) / variability (standard deviation divide by square root ...
The solution examines solving significance levels during recent major league baseball seasons.
Car Dealership, Level of Significance, Digital Camera
4. Car dealership chain owner wants to increase the car sales of his chain. He wants to determine which factors influence the sales performance. Owner thinks that the following factors have a significant impact on sales performance:
X1 = number of years of experience as a car sales person
X2 = age
Sales performance is measured as number of cars sold per year Y.
Owner selects twenty sales associates at random. Their past sales performance, number of years of experience, and age were retrieved from dealership records. Owner hires a statistician who enters the data into statistical software package and the following equation is obtained:
Y' = 9.606 + 1.998X1 + 0.222X2
A. How is this equation called?
B. How many independent variables are there in this equation? How many dependent variables?
C. What is the number 1.998 called?
D. As number of years of experience (X1) increases for one year, how much will estimated number of cars sold per year increase.
E. Michael Pendergrass applied for a sales associate position. He has been a car salesman for ten years and he is 37 years old. Estimate annual numbers of cars per year Michael would sell if he was hired.
5. Experiment was conducted at the .01 level of significance. The one-tailed test with the rejection area in the upper tail of the z-curve was used. Computed z-score was 1.79. What does it mean?
A. We should reject H0 and accept H1.
B. We should not reject H0.
C. We should have used the .05 level of significance.
D. We should increase the sample size.
6. A new model of digital camera is marketed in three major department store chains. The number of cameras sold every month at each of three store chains is listed below.
Target K Mart Wal Mart
177 164 180
200 144 213
191 170 198
188 151 204
At 0.05 level of significance, is there a difference in the mean numbers of cameras sold at the three department store chains?
A. State the null and the alternative hypothesis.
B. Compute SS total, SST, and SSE.
C. Develop an ANOVA table
D. What is the decision regarding the null hypothesis (is there a difference in the mean numbers of cameras sold at the three department store chains)?
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