Question

5. You run a small business, and you believe that your revenues have been going up. In the past you made an average of $4500 each week. You have recently taken the data on the revenue for 30 weeks and calculated a mean of $5300 and a standard deviation of $1700. A) State your null and alternative hypotheses B) Carry out the test with α-0.05 C) What would it mean if the truth was that your revenues had not gone up?

Answer 1

Answer

(A) Claim is that the revenues have been going up, so we will assume that mean is greater than $4500 for alternate hypothesis and for null hypothesis, we assume that the revenues had not gone up, so we can say that the mean is equal to $4500

Ho : μ = 4500

This a right tailed hypothesis testing.

(B) We have to use the t test statistic as population standard deviation is unknown in this case

Formula for t test statistic is given as

t statistic =

where

(5300-4500)/( 1700/v/30) = 800/310.38 = 2.58

Degree of freedom = n-1 = 30-1 = 29

Now, using the t statistic value of 2.58 and degree of freedom 29, we get

p value = 0.0076 (using t distirbution table)

So, it is clear that p value is less than 0.05. Result is significant and we can reject the null hypothesis.

So, we can conclude that there is enough evidence to support the claim.

(C) If the truth was that revenues had not gone up, then we have to test claim and in that case, we have insufficient evidence to support the claim that the revenues had not gone up because the hypothesis testing shown us that there is an increase in revenues.