# Sample Essay on Report

The statistical issue facing Mr. Plex and his competitors in the movie industry is hypothesis testing. The parameter to be tested here is the number of movie goers who are unhappy with the commercials against those who seem okay with the commercials. Since the owners are faced with the problem of clearly determining the percentage of those happy and those like Tommy who are not impressed by the commercials, a sample mean will be required to provide an unbiased estimate of the population mean. This implies that the owners will have to randomly select a sample to represent the population of the moviegoers visiting their theaters.

The sample selected will be useful in determining the overall views of the population of moviegoers who have encountered the issue of commercials being shown before the movie they paid for. The number of times the moviegoers have felt offended by the commercials will be compared against those who felt comfortable in spite of the commercials. From the hypothesis testing, the consortium will be guided by the results possibly discussed with statistician since the consortium seems to be unaware of how they will interpret the results and draw useful inferences from the findings. The result will go a long way in helping the owners reach a decision on whether to take claims by Tommy seriously or whether to ignore the claims. This is because they will be convinced from the facts that the lawsuit filed will in no way affect their business operations and that they will not incur heavy financial losses acquiring the services of defense lawyers.

##### Calculations

Suppose the consortium works with a sample size (n) of 800 movie goers and out of this they find out that 48 movie goers are in support of Tommy, the z statistic and p-value will be calculated as follows:

Percentage supporting Tommy (P*) =×100

= 6% =0.06

The percentage to test significance of Tommy’s claims (P) = 10% =0.1

Therefore: Z=

Z=

Z= 0.015

P-value= 0.0199

At the chosen level of significance, that is, 5% or 0.05, the p-value is less than the significance level thereby Mr. Plex and the rest of the consortium will be motivated to proceed with the proceedings of the law suit. From their discussion, the owners result to the agreement that if the percentage of those unhappy is greater than 10 % or more, they will consider negotiating for a settlement of the lawsuit filed by Tommy but if the percentage is less than ten, then they will have the courage to push forward with the case. A smaller discrepancy between the sample mean and the population mean will prove that the claims made by Tommy are true.

The null and alternative hypotheses will be have to be stated. The null hypothesis will be that moviegoers are happy with the commercials whereas the alternative hypothesis will be that moviegoers are not happy with the commercials. A t distribution will be appropriate for the statistical findings since it would provide the extent to which the sample mean is far from the population means using the standard deviation. The larger the value of the t statistic the further a sample mean is from the population mean stated in the null hypothesis.

The t distribution will therefore provide the solution to the problem of how the consortium will use the results from the survey. According to their agreement, if the probability of obtaining a sample mean is less than 10% when the null hypothesis is true, then the decision will be to reject the null hypothesis meaning the owners will have to brace themselves for legal war with Tommy and the likes who may desire to be enjoined in the case. If the probability of obtaining a sample mean is greater than 10% when the null hypothesis is tested, then the consortium will be relieved. This is because the null hypothesis will be retained and the statistical findings will be that a significant population of moviegoers is satisfied by the fact that the theaters show commercials before the audience view the movie paid for.