Question

g Cell phones. Following are last year's local monthly bills, in dollars, for a random sample of 50 cell phone users. 32.88,31.09.16.13,104.2,47.65,116.96,61.97,43.74,13.52,15,37,30.09,16.93,44.67,28.08,64.68, 16.17,28.04,57.67,14.62,61.32,35.64,88.95,50.48,16.41,16.56,13.48,27.10,15.50,19.95,23.45,4 6.24,41.8,49.35,81.16,28.80,32.48,28.95,31.60,35.6,24.74,44.82,51.62,42.04,22.43,46.54,48.3 2,24.53,77.21,15.12,126.84 At the 5% significance level, do the data provide sufficient evidence to conclude that last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.37

Answer 1

At 5% significant level, there is sufficient evidence to suggest that last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.37

Explanation:

The given data are presented as follows;

32.88, 31.09, 16.13, 104.2, 47.65, 116.96, 61.97, 43.74, 13.52, 15, 37, 30.09, 16.93, 44.67, 28.08, 64.08, 16.17, 28.04, 57.67, 14.62, 61.32, 35.64, 88.95, 50.48, 16.41, 16.56, 13.48, 27.10, 15.50, 19.95, 23.45, 46.24, 41.8, 49.35, 81.16, 28.80, 32.48, 28.95, 31.60, 35.6, 24.74, 44.82, 51.62, 42.04, 22.43, 46.54, 48.32, 24.53, 77.21, 15.12, 126.84

We note that there are 51 data points, however, the points, 15 and 37 are given without decimal place values and therefore, they are taken as one data point to make 50 data points.

The given sample size = 50

The mean mean of the given data,
`\overline x` ≈ 41.01

The standard deviation of the given data, s ≈ 26.59

The null hypothesis, h₀; μ = 47.37

The alternative hypothesis, hₐ; μ < 47.37

The significant level, α = 5%

Therefore, we have;

The test statistics is given as follows;

`t=\frac{\bar{x}-\mu }{(s)/(√(n))}`

Plugging in the values gives;

`t=(41.01-47.37)/((26.59)/(√(50))) \approx -1.69131`

The critical-t at 5% at df = n - 1 = 51 - 9 = 49 degrees of freedom and significance level, α of 5% (0.05) from a calculator = -1.676551

Given that the test statistic is larger than the critical-t, we therefore reject the null hypothesis. There is enough statistical evidence to suggest that last years mean monthly bill for cell phone users has decreased from 2001 mean to $47.37.