Question

1. A craft brewer sells beer in 2 nearby towns. Some months, he sells more in Town 1 & other months hesells more in Town 2. However, he is pretty sure that he usually sells more in Town 1. So, he has set up the following hypothesis test. He has also looked up the sales figures from the last 30 months in both towns and calculated some sample statistics. Those are below too. Use this information to answer/do the following.

H₀ : µ₁− µ₂ ≥ 0

H_a : µ₁− µ₂< 0

Town #1 (population 1)	Town #2 (population 2)
n1 = 30	n2 = 30
x¯1 = $31,000	x¯2 = $28,500
σ1 = $5,000	σ2 = $6,000

1. Estimate the mean difference.
2. Provide a 90% confidence interval for this mean difference.
3. Provide a 95% confidence interval for this mean difference.
4. Provide a 99% confidence interval for this mean difference.
5. What is the value of the test statistic (the z-value)?
6. What is the p-value? Round to 4 decimal places.
7. At the 90% level (α = 0.10), does he Reject H₀ or Fail to reject H₀?
8. At the 99% level (α = 0.01), does he Reject H₀ or Fail to reject H₀?

Answer 1