Question

13. A manufacturer of car batteries claims that his product will last at least 4 years on average. A sample of 50 is taken and the mean and standard deviation are found. The test statistic is calculated to be -1.82. Using a 5% significance level, the conclusion would be:

    1. There is sufficient evidence for the manufacturer's claim to be considered correct.

    2. There is insufficient evidence for the manufacturer's claim to be considered correct.

    3. There is sufficient evidence for the manufacturer's claim to be considered incorrect.

    4. There is insufficient evidence for the manufacturer's claim to be considered incorrect.

Answer 1

A manufacturer of car batteries claims that his product will last at least 4 years on average.

Therefore, the null and alternative hypotheses are,

H0 : μ ≥ 4 (claim)

Ha : μ < 4

Sample size (n) = 50

Test statistic = Z = -1.82

Significance level = 0.05

Using standard normal z-table we get, critical value at significance level of 0.05 is, Z^* = -1.645

Since, test statistic = -1.82 is less than -1.645, we reject the null hypothesis (H0).

Therefore, there is sufficient evidence for the manufacturer's claim to be considered incorrect.