185k views
4 votes
A department store wants to know what fraction of its customers in a certain market have store credit cards, and what their average balance might be. Of the 120 customers surveyed, 30 had store credit cards. Amongst those customers, the average balance was $600, with a sample standard deviation of $80. Find the 98% confidence interval for the average credit card balance. ( , ) Round your answers to two decimal places.

User LambdaBeta
by
8.8k points

1 Answer

2 votes

Answer:

The 98% confidence interval for the average credit card balance is

(564.04, 635.96).

Explanation:

We have to calculate the 98% confidence interval on the average credit card balance.

The sample will consist of the n=30 customers that have credit card.

The sample has a mean of $600 and a standard deviation of $80.

As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.

The degrees of freedom are:


df=n-1=30-1=29

The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).

Then, the margin of error is:


E=t\cdot s/√(n)=2.463*80/√(30)=197.04/5.48=35.96

Then, the upper and lower bounds of the confidence interval are:


LL=\bar X-E=600-35.96=564.04\\\\UL=\bar X+E=600+35.96=635.96

User Egorulz
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories