Question

A cell phone company states that the mean cell phone bill of all their customers is less than $83. A sample of 19 customers gives a sample mean bill of $82.17 and a sample standard deviation of $2.37. At ? = 0.05 , test the company’s claim?

1). State the hypothesis and label which represents the claim: : H 0 : H a

2). Specify the level of significance  =

3). Sketch the appropriate distribution, find and label the Critical Value(s) in Statdisk to 3 decimal places, and shade in  to indicate the Rejection Region(s)

4.) Calculate the test statistic (to 3 decimal places). Label this appropriately as Z or t.

5). Decision: Reject Ho or Do Not Reject Ho (You do not have to write a statement):

6). In the distribution below, label the test statistic you calculated from part (4). Using Statdisk, find the P-value corresponding to the test statistic. Shade in and label the P-value in the distribution.

Answer 1

Solution :

= 83

= 82.17

s = 2.37

n = 19

This is the left tailed test .

The null and alternative hypothesis is

H0 :   = 83

Ha : < 83

= 0.05  

The critical value for a left-tailed test is tc​=−1.734.

The rejection region for this left-tailed test isR =t : t<−1.734

Test statistic = t

= ( - ) / s / n

= ( 82.17- 83) / 2.37 / 19

= -1.527

P (Z < -1.527 ) = 0.0721

P-value = 0.0721

= 0.05  

p=0.0721 ≥ 0.05

Do Not Reject Ho.

There is insufficient evidence to suggest that