Question

A manufacturing company claims that its new designed batteries last at least sixty hours on average in any smart phone which is currently on the market. Tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 57.8 hours with a standard deviation of 5.4 hours. Assume that the mean battery life is normally distributed.

Step 1 of 5: The appropriate set of hypotheses to be used to test the manufacturer's claim will be

Answer

A.) H₀: μ ≥  60, H₁: μ <  60

B.)H₀: μ ≤ 60, H₁: μ > 60

C)H₀: μ <  60, H₁: μ ≥60

D)H₀: μ = 60, H₁: μ ≠ 60

Step 2 of 5: At α = 0.01, the critical value for a right-tail test of her hypothesis is

Step 3 of 5: The value of the test statistic for the hypothesis is

Step 4 of 5: The p-value for the test of the hypothesis is

Step 5 of 5: What will be the decision for the test at a significance level of 0.01?

Answer 1

Option - A) H0: $\mu$> 60

H1: $\mu$ < 60

At alpha = 0.01, the critical value is t_{0.01 17 = -2.567}

The test statistic t = ($\bar x - \mu$)/(s/$\sqrt n$)

= (57.8 - 60)/(5.4/$\sqrt 18$)

= -1.728

P-value = P(T < -1.728)

= 0.0511

Since the test statistic value is not less than the critical value (-1.728 > -2.567), so we should not reject the null hypothesis.

There is sufficient evidence to support the manufacturee's claim.