STAT homework help

Question

In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $40 and standard deviation of $17. Construct a confidence interval at a 98% confidence level.

Give your answers to one decimal place. What am I missing? I keep working the problems and it is showing me first answer is incorrect in my homework but second is correct? which does not make sense. Can someone please break this down easily for me? I tried to reach out to my professor but no response...

Answer 1

The key to this question is knowing which distribution to use for inference on the test statistic Z or T. There are two hints:

1. You are given information that the sample is "bell-shaped," so I would use the Z distribution.
2. To compute the confidence interval, you will use the formula:
3. m ± z(α/2) * s/sqrt(n)

where m=40

α =.02

z(α/2) = 2.326347

s=17

n=13 --> sqrt(n)=3.605551

1. So using your values, we have

40 ± 2.326347 * 17/3.605551

Which results in the confidence interval:

[29.031385, 50.968614]

These results are in single floating point precision, so feel free to round according to the requirements of the homework system you are using.

Now, if the system assumes that the sample size is too small for this problem, then you are performing inference on the population and should be using a T distribution. You will replace z(α/2) = 2.326347 with t(12,α/2) = 2.680998

40 ± 2.680998 * 17/3.605551

[27.359223, 52.640777]