Question

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is not 30g. The mean weight for a random sample of 16b ball bearings is 28.4g with a standard deviation of 4.5g. At the 0.05 significance level, test the claim that the sample comes from a population with a mean not equal to 30g. Find the critical value(s) and critical region. Identify the null and alternative hypotheses, test statistic, critical value(s) and critical region, as indicated, and state the final conclusion that addresses the problem. Show all seven steps.

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The sample comes from a population with a mean equal to 30g.

Alternative hypothesis: Ha: The sample comes from a population with a mean not equal to 30g.

H0: µ = 30 versus Ha: µ ≠ 30

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 30

Xbar = 28.4

S = 4.5

n = 16

df = n – 1 = 15

α = 0.05

Critical value = - 2.1314 and 2.1314

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (28.4 - 30)/[4.5/sqrt(16)]

t = -1.4222

P-value = 0.1754

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the sample comes from a population with a mean not equal to 30g.

There is sufficient evidence to conclude that the sample comes from a population with a mean equal to 30g.