49. Identify the CONCLUSION of a hypothesis test of the following claim and sample data: Claim: "The mean number of customers per day before the advertising campaign is less than the mean number of customers per day after the advertising campaign." A local restaurant began an advertising campaign on August 1st hoping to increase business. A random sample of 5 days before the advertising began and a random sample of 5 days after the advertising started, and the number of customers was recorded. Assume that the number of customers per day in this restaurant both before and after the advertising campaign is normally distributed. Test the claim at the 0.01 significance level. $\begin{array}{cccccc}\text { Before } & \text { June 7 } & \text { July 1 } & \text { July 8 } & \text { July 10 } & \text { July 25 } \\ & 45 & 50 & 55 & 53 & 51 \\ \text { After } & \text { August 2 } & \text { August 9 } & \text { August 20 } & \text { September 2 } & \text { September 6 } \\ & 62 & 74 & 72 & 73 & 70\end{array}$

Step 1 ：Given the claim: 'The mean number of customers per day before the advertising campaign is less than the mean number of customers per day after the advertising campaign.'

Step 2 ：We are testing this claim at the 0.01 significance level using a hypothesis test for the difference between two means.

Step 3 ：The null hypothesis (H0) is that the mean number of customers per day before the advertising campaign is equal to the mean number of customers per day after the advertising campaign.

Step 4 ：The alternative hypothesis (H1) is that the mean number of customers per day before the advertising campaign is less than the mean number of customers per day after the advertising campaign.

Step 5 ：First, we calculate the mean and standard deviation for the number of customers per day before and after the advertising campaign. The mean before the campaign is \(50.8\) and the mean after the campaign is \(70.2\). The standard deviation before the campaign is approximately \(3.77\) and the standard deviation after the campaign is approximately \(4.82\).

Step 6 ：Next, we calculate the test statistic and the p-value. The test statistic is a measure of how far the sample mean is from the null hypothesis mean, and the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Step 7 ：If the p-value is less than the significance level, we reject the null hypothesis. This means that we have enough evidence to support the claim that the mean number of customers per day after the advertising campaign is significantly greater than before the advertising campaign.

Step 8 ：Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.

Step 9 ：Final Answer: The conclusion of the hypothesis test is that the mean number of customers per day after the advertising campaign is significantly greater than before the advertising campaign. Therefore, the advertising campaign was successful in increasing the number of customers per day. This is represented as \(\boxed{\text{Reject } H_0}\).