Question

1. Describe in full sentences the hypothesis testing steps & provide an example to solve by using hypothesis testing.

2. What does Type I and Type II errors mean?

3. 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 $0.28. A research was done to test the claim that the mean cost of a Starbucks Grande Caffe Latte is $3.65. Ten Starbucks Grande Caffe Latte yeld a mean cost of $3.48 with a standard deviation of $0.26. 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 write an appropriate

conclusion, using complete sentences.

i. Alpha:

ii. Decision:

iii. Reason for decision:

iv. Conclusion:

i. Construct a 95% confidence interval for the true mean or proportion.

Answer 1

3(a)

(b)

(c)

The random variable is the sampling distribution of sample mean cost of a Starbucks Grande Caffe Latte for sample size n=10.

(d)

Test is two tailed.

(e)

Since population standard deviation is known so standard normal distribution will be used.

(f)

Given information:

The test statistics is

(g)

The p-value is

p-value =2P(z < -1.92) = 0.0548

(h)

(i)

(ii)

Since p-value is greater than so we fail to reject the null hypothesis.

(iii)

The p-value is greater than .

(iv)

Conclusion: There is evidence to conlcude that the mean cost of a Starbucks Grande Caffe Latte is $3.65.