Question

• A manufacturing firm claims that the batteries used in their electronic games will last an average of 30 hours. To test this claim is accurate or not, a random sample of 16 batteries are tested. The observed sample mean ¯x = 27.5 hours and sample standard deviation s = 5. Assume the distribution of battery lives to be approximately normal. Conduct a 5step-hypothesis test. Use the significance level, α = 0.05.
  1. State the assumptions.
  2. Define the parameter of interest and state the null and alternative hypotheses.
  3. Calculate the value of the test statistic. Interpret it in the context of the problem.
  4. The reported P-value is 0.064. Interpret it in the context of the problem.
  5. Draw the conclusion.
  6. [Multiple Choice] If the firm uses the same data to construct a 95% confidence interval, which one is the correct one? Explain why. (No calculation required).
     1. (24.8, 30.1)
     2. (25.5, 29.5)
     3. (23.1, 27.5)

Answer 1

Here we have to test that

Null hypothesis:

Alternative hypothesis:

where

Sample size = n = 16

Sample mean = = 27.5

Sample standard deviation = s = 5

a)

Assume the distribution of battery lives to be approximately normal.

Here population standard deviation is not known so we use t test.

b)

Parameter of interest : Average battery lives

c)

Test statistic:

t = -2   

Test statistic = t = -2

d)

P-value = 0.064

Level of significance = = 0.05

Here p value >

So we fail to reject H0.

e)

Conclusion: There is sufficient evidence to conclude that the batteries used in their electronic games will last an average of 30 hours.

f)

Confidence level = c = 0.95

95% confidence interval is

where tc is t critical value for c = 0.95 and degrees of freedom = n - 1 = 16 - 1 = 15

tc = 2.131 (From statistical table of t values)

(Round to one decimal)

95% confidence interval is (24.8, 30.2)

Option A is correct.