The cost of a Starbucks Grande Caffe Latte varies from city to city. However, the variation among prices remains steady with a standard deviation of $0.26. A research was done to test the claim that the mean cost of a Starbucks Grande Caffe Latte is at least $3.65. Ten Starbucks Grande Caffe Latte yield a mean cost of $3.48 with a standard deviation of $0.18. Do the data support the claim at 5% level?
a. State the H0:
b. State the Ha:
c. In words, CLEARLY state what your random variable X ¯ or P′ represents.
d. Is this a right-, left-, or two-tailed test?
e. State the distribution to use for the test.
f. What is the test statistic?
g. What is the p-value? In one or two complete sentences, explain what the p-value means for this problem.
h. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and provide an appropriate conclusion, using complete sentences.
i. Alpha:
ii. Decision:
i. Construct a 95% confidence interval for the true mean or proportion.
iii. Reason for decision:
iv. Conclusion: