Question

A movie theater manager wants to determine whether popcorn sales have increased since the theater switched from using "butter-flavored topping" to real butter. Historically the average popcorn revenue per weekend day was approximately $3,500. After the theater started using real butter, the manager randomly sampled 12 weekend days and calculated the sample’s summary statistics. The average revenue per weekend day in the sample was approximately $4,200 with a standard deviation of $140. Select the function that would correctly calculate the 90% range of likely sample means.
A. 3,500±CONFIDENCE.T(0.10,140,12)

B. 4,200±CONFIDENCE.T(0.10,140,12)

C. 3,500±CONFIDENCE.NORM(0.10,140,12)

D. 4,200±CONFIDENCE.NORM(0.10,140,12)

Answer 1

Answer:

The function that would correctly calculate the 90% range of likely sample means is given by:

B. 4,200±CONFIDENCE.T(0.10,140,12)

Step-by-step explanation:

In Microsoft Excel, the syntax

$CONFIDENCE.T(alpha,standard-dev,size)$  returns the confidence  interval for the population mean, using the students T-distribution.$Alpha=1-90\%=10\%=0.10$

The standard deviation is given as $140 and the sample size is 12.

In constructing the confidence  interval we use:

$\bar X\pm CONFIDENCE.T(alpha,standard-dev,size)$  

Let us substitute the values to get:

$4,200\pm CONFIDENCE.T(0.10,140,12)$

We use the T distribution because $\sigma$ is unknown