The mean price of a cup of coffee in Portland, OR is $2.67. The owner of a new coffee house believes that the mean price of coffee is different in their neighborhood. A sample of 10 coffee prices from other local coffee shops are shown below.

Price
2.22
3.78
3.78
4.89
3.59
2.1
1.73
4.26
4.17
3.04

Test the claim that mean price of a cup of coffee is not equal to $2.67 using a 5% level of significance. Assume that the coffee prices are normally distributed. Give answers to at least 2 decimal places.

a) Fill in the hypotheses below:

H₀: Select an answer σ σ² p̂ x̄ p s s² μ ? ≤ = > ≠ ≥ < $

H₁: Select an answer p̂ s² p s σ² μ σ x̄ ? ≤ ≠ > ≥ < = $

b) The p-value is 0.0681.

The correct decision is to Select an answer Reject the null hypothesis Fail to reject the null hypothesis Accept the null hypothesis Accept the alternative hypotheis .

The correct summary would be: Select an answer There is not enough evidence to reject the claim There is sufficient evidence to support the claim There is insufficient evidence to support the claim that the population mean price of a cup of coffee is not equal to $2.67.