Question

Data consistent with summary quantities in the article "Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children" on total calorie consumption on a particular day are given for a sample of children who did not eat fast food on that day and for a sample of children who did eat fast food on that day. Assume that it is reasonable to regard these samples as representative of the population of children in the United States.No Fast Food2325 1912 1003 1724 1463 2047 2137 19751846 1771 1759 1821 1642 1500 2663 Fast Food2527 1762 938 2332 2438 2271 2530 1199 894 1515 879 2211 1815 1254 2121 (a) Use the given information to estimate the mean calorie intake for children in the United States on a day when no fast food is consumed. (Give the answer to one decimal place.)Correct: Your answer is correct.(b) Use the given information to estimate the mean calorie intake for children in the United States on a day when fast food is consumed. (Give the answer to one decimal place.)Correct: Your answer is correct.(c) Use the given information to estimate the produce estimates of the standard deviations of calorie intake for days when no fast food is consumed and for days when fast food is consumed. (Give the answer to three decimal places.)No Fast Food is consumeds = Incorrect: Your answer is incorrect.Fast Food is consumeds =

Answer 1

To estimate the mean calorie intake for children in the United States on a day when no fast food is consumed, we calculate the mean of the no fast food sample. The mean calorie intake is 1873.9 calories. To estimate the mean calorie intake on a day when fast food is consumed, we calculate the mean of the fast food sample. The mean calorie intake is 1746.4 calories. We can estimate the standard deviations by applying the sample standard deviation formula. The standard deviation for no fast food days is 445.352 calories, and for fast food days it is 671.594 calories.

Step-by-step explanation:

To estimate the mean calorie intake for children in the United States on a day when no fast food is consumed, we need to calculate the mean of the data for the no fast food sample.

1. Add up all the calorie values for the no fast food sample: 2325 + 1912 + 1003 + 1724 + 1463 + 2047 + 2137 + 1975 + 1846 + 1771 + 1759 + 1821 + 1642 + 1500 + 2663.
2. Divide the sum by the number of data points in the no fast food sample, which is 15.
3. Rounded to one decimal place, the mean calorie intake for children in the United States on a day when no fast food is consumed is 1873.9 calories.

To estimate the mean calorie intake for children in the United States on a day when fast food is consumed, we need to calculate the mean of the data for the fast food sample.

1. Add up all the calorie values for the fast food sample: 2527 + 1762 + 938 + 2332 + 2438 + 2271 + 2530 + 1199 + 894 + 1515 + 879 + 2211 + 1815 + 1254 + 2121.
2. Divide the sum by the number of data points in the fast food sample, which is 15.
3. Rounded to one decimal place, the mean calorie intake for children in the United States on a day when fast food is consumed is 1746.4 calories.

To estimate the standard deviations of calorie intake for days when no fast food is consumed and for days when fast food is consumed, we can use the sample standard deviation formula.

1. Calculate the variance for each sample by subtracting the mean from each data point, squaring the result, and summing the squared differences.
2. Divide the sum of squared differences by the number of data points minus 1 for each sample to calculate the sample variances.
3. Take the square root of each sample variance to calculate the sample standard deviations.
4. Rounded to three decimal places, the standard deviation for days when no fast food is consumed is 445.352 calories, and the standard deviation for days when fast food is consumed is 671.594 calories.