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Literature & Language

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Math Problem

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English (U.S.)

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# Inferential Statistics (Math Problem Sample)

Instructions:

This is an Inferential Statistical Paper Analysis on how to test for hypothesis.

source..Content:

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 Î» =0.02, we can agree that there is evidence to reject the manufacturerâ€™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

áµª =745hrs

â€‚=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 (Î»=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...

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