Answer to Question #138866 in Statistics and Probability for ike

Question

The average monthly cell phone bill was reported to be Php 2,400.00. Random sampling of a large cell phone company found the following monthly cell phone charges.

2,679.85 2,461.00

2,902.56 3,023.25

2,812.80 2,361.50

2,394.20 3,380.16

2,517.60 2,403.95

At the .05 level of significance, can it be concluded that the average phone bill has increased?

Answer 1

solution

$$population\ mean, \mu = 2400$$

$$Sample\ mean, \bar x=\frac{1}{n}\sum x_i= 2693.687$$

$$Sample\ sd, \sigma=\sqrt{\frac{1}{n-1}\sum (x_i- \bar x)^2}=334.4984$$

The test statistic

$$Z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}$$

$$\frac{2693.687-2400}{\frac{334.4984}{\sqrt{10}}}=2.7765$$

At a 95% level of confidence, we reject the hypothesis that there is no change if Z > 1.96

answer: we conclude that the average phone bill increased since 2.7765 > 1.96