# Case 302 July in Multiplex

#### Case 302

From this case, there are two types of errors, which the consortium can make. A Type I Error is referred to as a “false positive. ” A Type I error would be made when the null hypothesis is rejected when it should be accepted. This error may occur if the consortium defends any lawsuit against them if they are using 6% (6/100) as their surveying result. The results of the sample size of 100 people indicate that the percentage range is from 1. 35% to 10. 65%. The test results can be higher than 10%, but actually it is lower. Therefore, if the consortium defends any lawsuit against them it is possible that a Type I Error can be made. The second type of error is a Type II Error, which is also known as “false negative. ” A Type II error would be made when the alternative hypothesis is rejected when it should be accepted. For this to occur, the consortium must make a decision to settle the case when the survey result shows a lower percentage than 10% but in reality, it is actually higher than 10%. The only error the consortium should make is a Type II error because the alternative hypothesis was rejected. As previously stated, using a sample size of 100 shows that we would not reject the null hypothesis, in other words, this would mean to settle with Tommy. If we did not create a second hypothesis test using a sample size of 300, we would not have defended against.

Tommy in court and a Type II error would have been made.

 Size of simple Defend lawsuit| Settlement 100 Type II Error Right decision 300

We have proven that 94% of the surveyed moviegoers indicated that they are satisfied that theater plays commercials before the movie. Only 6% of the moviegoers opposed watching commercials before the movie. This statistical analysis validates that the consortium should seek to defend any lawsuit Tommy or any other unhappy moviegoer files. In this situation, a Type II error would have been made if we decided to base our analysis only on a sample size of 100. A larger sample size always depicts a more accurate display.

#### Statistical Analysis

• H0 = 10% H1 < 10% 1st
• Same Size N: 100 (sample size) p? : 6/100 = . 06
• Confidence Interval .06 1. 96 = . 0135 — . 1065

#### Test Statistic

• Z= = -1. 33, from Standard Normal Distribution table => P-value = . 0918 P-value > (alpha) .0918 > . 05
• Since P-value (. 0918) is greater than alpha (. 05), we fail to reject the null hypothesis.
• Sample Size N: 300 p? : 18/300 = . 06
• Confidence Interval .06 1. 96 = . 0331 — . 0869
• Test Statistic Z= = -2. 31 from Standard Normal
• Distribution table => P-value = . 0104 P-value < alpha .0104 < . 05
• Since P-value (. 0107) is less than alpha (. 05), we reject the null hypothesis

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