Question

Question 4 [25]

The Zambezi car battery manufacturer claims that the average lifespan of batteries produced by his firm is at least 30 months. The rival manufacture the Rehoboth batteries disagree and took random sample of 100 Zambezi car batteries and recorded a mean of 31.7 months and a standard deviation of 8 months. (Show all your works)
Determine the following: a) The null and alternative hypotheses 3 b) The test statistic value. 5 c) The critical statistics value at 99% confidence level 5

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d) The rejection region using critical value approach 2 e) The p value at 99% confidence level 5 f) The rejection region using both the p value approach 2 g) Make conclusion about the population mean using both approaches 3

Answer 1

x̅ = 31.7,  s = 8, n = 100

α = 0.01

a) Null and Alternative hypothesis:

Ho : µ ≥ 30

H1 : µ < 30

b) Test statistic:

t = (x̅- µ)/(s/√n) = (31.7 - 30)/(8/√100) = 2.1250

df = n-1 = 99

c) Critical value :

Left tailed critical value, t-crit = T.INV(0.01, 99) = -2.365

d) Reject Ho if t < -2.365

e) p-value :

Left tailed p-value = T.DIST(2.125, 99, 1) = 0.9820

f) Reject Ho if p-value < 0.05

g) Conclusion:

As t > -2.365, Do not reject the null hypothesis.

As p-value > α, Do not reject the null hypothesis.