Inferential Statistics (Math Problem Sample)

Statistics
[Name]
[Institutional Affiliation]
Problem
A light bulb manufacturer guarantees that the mean life of a certain light bulb is at least 750 hours. A random Sample of 36 light bulbs has a mean life of 745 hours with a standard deviation of 60 hours.
The problem requires that we determine whether at λ =0.02, we can agree that there is evidence to reject the manufacturer’s claim, find the test statistic, the p-value, decide if we can reject the null hypothesis, and interpret the decision in the context of the original claim.
Calculations
Steps followed are as follows;
From the question presented alongside, the following can be deducted;
n=36
µ=750hrs
ᵪ =745hrs
 =60
Hypothesis testing;
In hypothesis testing we present both the null and alternative hypothesis; and prove their worthiness if true or false. Depending on what to test, we accept or accept the null hypothesis as shown below;
Claim: H0: The mean half-life of light bulb is at least 750Hrs
H1: The mean half-life of light bulb is less than 750Hrs
H0 = µâ‰¥750Hrs
H1 = µ<750Hrs
This can be tested using a one tailed test in which alpha (λ=0.02). Hence,
To find the statistic;
P=, and hence, p=, = -0.5
Consider the diagram below;
0.02
Z= -2.05
From the calculation in the z-tables z= -2.05 an...