Question

To estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. A graph of the sample data showed an approximately symmetric distribution with no outliers. The sample mean and standard deviation were $734 and $102, respectively. The journalist will create a 95 percent confidence interval to estimate the population mean. Have all conditions for inference been met?
A. Yes, all conditions have been met.

B. No, the 15 weddings in the sample were not selected at random.

C. No, the sample size is not large enough to assume the sampling distribution of sample means is approximately normal.

D. No, because the graphical display is approximately symmetric it cannot be assumed that the sampling distribution of sample means is approximately normal.

E. No, the sample size of 15 is not less than 10 percent of all weddings in the state.

Going between C and D.

Answer 1

Answer:

C and D are both correct (if only one option can be selected then select C)

Explanation:

The conditions for inference is as follows:

1. The data has to be from a random sample
2. The data has to be in a normal distribution
3. The observations need to be independent of one another

From the information we have, it seems that conditions 1 and 3 have been met. The cost of flowers at each wedding is not dependent on another wedding, and the weddings appear to be selected at random across the state.

However, 15 weddings is a small sample size, and it would be difficult to determine normal distribution from this number. Therefore, C could be correct. Additionally, just because the distribution is symmetric doesn't mean it is normal. A normal distribution is when a histogram of the data makes a bell-shape. However, data can be symmetric and not bell-shaped. Therefore, D is the correct answer.