Question

Test the claim that the majority of people owe at least $1,000 to Visa

The data collected below comes from people that live in Salinas. Listed below are the genders, ages and current balance on one specific type of Visa card.

Gender	Balance	Age
M	235	19
M	122	24
M	1752	55
M	1543	62
M	1655	34
M	0	19
M	84	22
M	355	26
M	299	28
M	2404	45
M	848	54
M	667	71
M	1248	32
M	7746	38
M	0	41
M	8329	51
M	486	34
M	554	38
M	874	54
F	601	62
F	56	80
F	472	27
F	59	18
F	4233	49
F	2544	58
F	109	22
F	235	24
F	644	36
F	3484	57
F	1509	27
F	624	30
F	3324	59
F	2268	33
F	495	19
F	0	26

Answer 1

The claim here is that "the majority of people owe at least $1,000 to Visa". Here, majority means more than 50% of people. In the given data, there are n=35 observations and out of 35, there are 13 people who owe at least $1000 to Visa. Therefore by translating these in Statistical terms we have

Null hypothesis:

Alternate hypothesis:

Level of significance:

Test statistic: will follow a Standard Normal distribution.

Critical region is

Since the calculated Z value doesn't fall in the critical region, we fail to reject the Null hypothesis. Hence, we conclude that there is not enough evidence to claim that a majority of the people owe at least $1000 to Visa.