Question

14. Claim: The average cost to repair a smart phone is less than $100. Test at α = 0.1. Data: 7 smart phone repairs are chosen at random. The average of these is $95.56, with a standard deviation of $20.

(a) Are these data statistically significant evidence to support the claim?

(b) Are these data statistically significant evidence to refute the claim?

Answer 1

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

The null and alternative hypotheses are given as below:

H₀: µ = 100 versus H_a: µ < 100

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 100

Xbar = 95.56

S = 20

n = 7

df = n – 1 = 6

α = 0.10

Critical value = -1.4398

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (95.56 - 100)/[20/sqrt(7)]

t = -0.5874

P-value = 0.2892

(by using t-table)

P-value > α = 0.10

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average cost to repair a smart phone is less than $100.

(a) Are these data statistically significant evidence to support the claim?

Answer: No

(b) Are these data statistically significant evidence to refute the claim?

Answer: Yes