Question

According to a recent article about individuals who have credit cards, the mean number of cards per person with credit cards is 4. To test this result a random survey of 60 individuals who have credit cards was conducted. The survey only includes the number of credit cards per participant. Do the results of the survey imply that the mean number of cards per individual is less than 4? Use 0.05 as the level of significance. Determine the t-statistics (round to two decimal places). Determine the P-value(round to three decimal places). Make a conclusion in regards to the null. I tried posting a pic of the data for this question but for whatever reason it would not post/upload so the data is as follows 4,1,2,4,3,2,2,9,4,4,2,4,2,2,4,4,3,2,2,2,3,4,7,3,3,2,3,1,2,3,3,4,4,2,3,3,2,2,17,6,2,2,4,9,3,2,2,4,2,1,6,4,3,3,3,8,3,4,4,2

Answer 1

From the given sample data :

The sample size is , n=60

The sample mean is ,

The sample standard deviation is , s=

The null and alternative hypothesis is ,

The test is one-tailed test.

The test statistic is ,

Now , df=degrees of freedom=n-1=60-1=59

The p-value is ,

p-value= ; The Excel function is , =TDIST(1.57,59,1)

Decision : Here , p-value=0.061>0.05

Therefore , fail to reject Ho.

Conclusion : the results of the survey does not imply that the mean number of cards per individual is less than 4.