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

a) Calculate the sample mean, median, mode and range to the nearest whole number.

b) Calculate the difference between the sample mean monthly cable bill and HORIZON’s population mean.

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

(a)

(i)

Sample mean () is given by:

    = 94 (Round to the nearest whole number.)

So.

Sample mean = 94

(ii)

Arranging numbers in asceding order, we get:

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

Median is (10+1)/2th item = Average of 5th & 6th item =(79 + 88)/2 = 83.5 = 84 (Round to the nearest whole number.)

So,

Sample median = 84

(iii)

There is no mode for this dataset because each valuue occurs only once.

(iv)

Range = Maximum -Minimum = 175 - 65 = 110

So,

Sample range = 110

(b)

= 94 - 75 = 19

So,

the difference between the sample mean monthly cable bill and HORIZON’s population mean = 19

(c)

H0:Null Hypothesis: 15 ( The difference between the sample mean and population mean is not greater than 15 dollars )

HA: Alternative Hypothesis: 15 ( The difference between the sample mean and population mean is greater than 15 dollars ) (Claim)

From the give data, we get:

s = Sample Standard Deviation = 33.3568

Take = 0.05

df = 10 - 1 = 9

From Table critical value of t = 1.833

Test Statistic is given by:

Since calculated value of t = 0.379 isless than critical value of t = 1.833, the difference is not significant.Fail to rejectnull hypothesis.

Conclusion:
The data do not support the claim that the difference between the sample mean and population mean is greater than 15 dollars. So, the consumer group does not have reason to dispute HORIZON’s report.