8a) Is the following statement correct or incorrect? Because the sample size of

Question

8a) Is the following statement correct or incorrect?
Because the sample size of 1238 is large enough, we can conclude that the distribution of the number of calories per order for the population of all Chipotle customers in Minneapolis is approximately normal.

8b) Provide the value that best completes the following statement:
The estimated average distance by which all possilbe values of the sample mean number of calories per order vary from the population mean number of calories per order is roughly ____________ calories per order.

254.154

1057.672

7.2233

1070

-1.7068

8c) Provide the value that best completes the following statement:
The sample mean number of calories per order is __________ (null) standard errors below the hypothesized population mean number of calories per order.

254.154

1057.672

7.2233

1070

-1.7068

8d) Provide the value that best completes the following statement:
The number of calories per order in the sample vary from the mean number of calories per order of 1057.672, by about _________, on average.

254.154

1057.672

7.2233

1070

-1.7068

8e) Select all correct interpretation(s) for the p-value = 0.04406

The probability the mean number of calories per order for all Chipotle customers in Minneapolis is 1,070 calories per order is 0.04406

Assuming the mean number of calories per oder for all Chipotle customers in Minneapolis is 1,070 calories per order, and if this inference procedure were repeated many times, we would expect the see a t test statistic of -1.7068 or less in only about 4.406% of repetitions.

Assuming the mean number of calories per oder for all Chipotle customers in Minneapolis is 1,070 calories per order, the probability of obtaining a t test statistic of -1.7068 is 0.04406.

Assuming the mean number of calories per order for all Chipotle customers in Minneapolis is 1,070 calories per order, the probability of obtaining a t test statistic of -1.7068 or less is 0.04406.

8f)John Thompson, the Chipotle area manager in Minneapolis, Minnesota who ran the new study, does not remember much from his introductory statistics course taken many years ago. He collected the data and run the data analysis using R, but does not understand the output. Write a brief email (3 to 4 sentences) to John Thompson to address the following topics in context:
1. Descriptive summary about the number of calories per order for Minneapolis Chipotle customers.
2. Conclusion regarding the results of the test (how Minneapolis customers compared to the reported finding in the New York Times article).

A recent article in the New York Times published a data analysis of 3,000 meals ordered at Chipotle and detemined that the average order contains 1,070 calories, which is more than half the total number of calories a person is supposed to eat in full day. These findings are based on 3,000 meals ordered by actual customers using the online deliviery service GrubHub from two Chipotles, one in Washington, D.C., and one in East Lansing, Michigan. A Chipotle area manager in Minneapolis, Minnesota (John Thompson) read the article and wondered if this also holds for Chipotles in Minneapolis which is voted the healthiest city in the US by Forbes magazine. The manager decided to run their own test. Using a 5% significance level, the manager would like to assess if, on average, the total number of calories per order for all Chipotle orders in Minneapolis is less than the reported finding in the New York Times article, that is Ho: = 1070 calories versus Ha:

Explanation / Answer

8 a )  Because the sample size of 1238 is large enough, we can conclude that the distribution of the number of calories per order for the population of all Chipotle customers in Minneapolis is approximately normal.

-------------------------------- TRUE .

8 b )  The estimated average distance by which all possilbe values of the sample mean number of calories per order vary from the population mean number of calories per order is roughly 7.2233 calories per order.

8 c )  The sample mean number of calories per order is -1.7068 (null) standard errors below the hypothesized population mean number of calories per order.

8 d )  The number of calories per order in the sample vary from the mean number of calories per order of 1057.672, by about 254.154 , on average.

8 e ) Assuming the mean number of calories per oder for all Chipotle customers in Minneapolis is 1,070 calories per order, and if this inference procedure were repeated many times, we would expect the see a t test statistic of -1.7068 or less in only about 4.406% of repetitions.

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