Question

A health inspector was interested in determining if the mean noise levels of road construction sites is less than 90 decibels. To test this, the noise levels at 64 randomly chosen road constructions sites were measured in decibels. The sample mean noise level was 85 decibels, and the population standard deviation is 10 decibels. Use the five step testing method using α = .025 to test the claim that road construction sites have a mean noise level less than 90 decibels.

Answer 1

STEP 1

Claim:- road construction sites have a mean noise level less than 90 decibels.

it is a case of less than, so it is a left tailed hypothesis test

STEP 2

Critical value for alpha = 0.025 is -1.96 (using z table)

We will reject Ho if z statistic is less than -1.96

STEP 3

given that

test statistic =

STEP 4

it is clear that the z statistic is less than z critical, i.e. -4 < -1.96

therefore, we will reject the Null hypothesis

STEP 5

Since the null hypothesis is rejected, we can say that there is sufficient evidence to conclude that the road construction sites have a mean noise level less than 90 decibels.