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

Page 11 of 13

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.**

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
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