Question

HORIZON, a national TV provider, reports that today’s typical digital cable customer pays about $75 which is the population mean per month. A customer group decides to sample ten customers of HORIZON to determine if the company’s information is correct. The following list represents the consumer group’s sample data.

Monthly digital cable bill (data measured in dollars)

89, 112, 69, 75, 88, 115, 175, 70, 65, 79

1. a) Calculate the sample mean, median, mode and range to the nearest whole number.
2. b) Calculate the difference between the sample mean monthly cable bill and HORIZON’s population mean.
3. c) The consumer group decides to dispute the HORIZON statement if the difference between the sample mean and population mean is greater than 15 dollars. Does the consumer group have reason to dispute HORIZON’s report? Explain?

Answer 1

The given data with their squares and sorted order is presented for further calculations:

	Bill	x^2	sorted
	89	7921	65
	112	12544	69
	69	4761	70
	75	5625	75
	88	7744	79
	115	13225	88
	175	30625	89
	70	4900	112
	65	4225	115
	79	6241	175
Total	937	97811

The mean is given by

The median will be the average of 5th and 6th value ie

There is no mode in the data since none of the observations are repeating.

The maximum value in the data=175 and the minimum=65. Hence the range=175-65=110

b). The population mean bill is $75 and the difference between the sample mean monthly cable bill and HORIZON’s population mean is 93.7-75=18.7.

c). The consumer group decides to dispute the HORIZON statement if the difference between the sample mean and population mean is greater than 15 dollars. Does the consumer group have reason to dispute HORIZON’s report? Explain?

Here we are interested in testing the following hypothesis:

(since the consumer group decides to dispute the statement if the difference is greater than $15 ide 75+15=90)

Level of significance:

The critical region is

Test statistic: follows a t-distribution with n-1 df.

Since the calculated value of t does not fall in the rejection region, we fail to reject the null hypothesis. Hence we conclude that there is not enough evidence in the claim of the consumer's forum to dispute the HORIZON statement if the difference between the sample mean and population mean is greater than 15 dollars.

Therefore the consumer group doesn't have reason to dispute HORIZON's report.