Interstate Batteries are supposed to last at least 3 years. A consumer advocate collects a random...

Interstate Batteries are supposed to last at least 3 years. A consumer advocate collects a random sample of 200 of these batteries and finds that 186 last at least 3 years. Does this provide evidence at the 5% significance level to support the claim that less than 95% of all Interstate batteries last at least 3 years? Justify by running a hypothesis test.

Solutions

Expert Solution

Proportion = 0.95
Total number of sample (n) = 200
number of favourable events (X) = 186

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (0.09717803482326515)
P = 0.0972

Here, the P-value is greater than the level of significance 0.05;
Fail to reject the null hypothesis

or,
Since, the test is two-tail test at

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.6448536269514722 or greater than the critical value 1.6448536269514722
The statistic value, -1.2978 is greater than the critical values -1.6448536269514722 .
Therefore, we fail to reject the null hypothesis.

orchestra answered 11 months ago

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