Question

The average monthly cell phone bill was reported to be $49.5.

Random sampling of a large cell phone company found the following monthly cell phone charges: 55.83, 49.88, 62.98, 70.42, 58.60, 51.29, 60.47, 52.45, 49.20, 50.02.

Calculate the sample mean and the sample standard deviation using Excel Functions.At the 0.05 level of significance can it be concluded that the average phone bill has increased?

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The average phone bill has not increased.

Alternative hypothesis: Ha: The average phone bill has increased.

H0: µ = 49.5 versus Ha: µ > 49.5

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 49.5

Xbar = 56.114

S = 6.972469991

n = 10

df = n – 1 = 9

α = 0.05

Critical value = 1.8331

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (56.114 – 49.5)/[ 6.972469991/sqrt(10)]

t = 2.9997

P-value = 0.0075

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the average phone bill has increased.