Question

How Big Is the Tip Percentage at a Restaurant? Use technology and the RestaurantTips dataset to find a 95% confidence interval for the mean tip percentage (PctTip) at the restaurant. Click here for the dataset associated with this question. Round your answers to two decimal places. The 95% confidence interval is (x) Office Update To keep up-to-date with security updates, fi) Office Update To keep up-to-date with security updates,

Answer 1

To find a 95% confidence interval for the tip percentage at a restaurant, use the provided information on confidence intervals. If the sample mean is 41, the 95% confidence interval is (67.02, 68.98). If the sample size is 50, the 95% confidence interval would be (66.86, 69.14).

Step-by-step explanation:

To find a 95% confidence interval for the mean tip percentage at a restaurant using the RestaurantTips dataset, we can use the provided information on confidence intervals. The 95% confidence interval is wider because the area 0.95 is larger than the area 0.90. This means that there is more certainty that the confidence interval contains the true value of the population mean.

Rounding to two decimal places, if the sample mean is 41, the 95% confidence interval would be (67.02, 68.98). The 90% confidence interval would be (67.18, 68.82).

If the sample size in the study was 50 instead of 30, the 95% confidence interval with a sample mean of 41 would be (66.86, 69.14).

Answer 2

A confidence interval presents a range where the true population parameter is likely to be found; to calculate it specifically for the mean, additional statistics are needed like standard deviation and sample size. An 18% tip converts to 0.18 as a decimal, which is then multiplied by the meal cost.

Step-by-step explanation:

A confidence interval provides a range of values within which we can be a certain percent confident that the true population parameter lies. When constructing a 95% confidence interval, you are including the central 95% of the probability of the normal distribution while excluding 2.5% on each tail.

To construct a 95% confidence interval for the mean when the sample mean is 41, you would need additional information such as the sample standard deviation and the sample size. The same goes for creating a 90% confidence interval. If the sample size were increased from 30 to 50, the interval would be narrower because increasing the sample size decreases the margin of error.

Converting a tip percentage to a decimal is a matter of dividing by 100. So, an 18% tip becomes 0.18 in decimal form, which can then be multiplied by the cost of the meal to find the total tip amount.