Question

3. [13 marks] Recall Question #2, Lab Report 3, where you sampled 200 Twitter stock prices. Suppose that you found the sample mean stock price to be c = $30.00 with a standard deviation of sc = $12.50.

(a) Suppose that a stock exchange has claimed that the true mean Twitter stock price is only $28. To test this claim, perform a hypothesis test at the α =0.02 significance level to determine whether the sample provides evidence that the true mean Twitter stock price differs from the stock exchange’s claim of $28. Be sure to state the null and alternate hypotheses and show your calculations of the test statistic (to 2 decimals) and p-value.

Null Hypothesis H0: Alternate Hypothesis Ha:

Observed test statistic:

p-value:

Conclusion:

Concluding Statement:

(b) For what levels of significance would the sample have provided evidence against the null hypothesis in part (a)?

(c) Construct a 98% confidence interval for the true mean Twitter stock price. Be sure to include units in your answer and make a concluding statement.

(d) Instead of using the "p-value" in part (a), could we have used the confidence interval in part (c) to test the null hypothesis? Explain why it could or could not be used and, if it could be used, how you would come to the same conclusion as in part (a).

(e) For each of the following, indicate the effect (circle the correct response) the proposed change would have on the center and width of the 100(1 − α)% confidence interval in part (c) for the true mean Twitter stock price (assuming all other relevant values stay the same).

			Center	Width
Decreasing the standard deviation.	decrease	same	increase	narrower	same	wider
Decreasing the sample mean.	decrease	same	increase	narrower	same	wider
Increasing the sample size.	decrease	same	increase	narrower	same	wider
Increasing the level of significance.	decrease	same	increase	narrower	same	wider
Increasing the level of confidence.	decrease	same	increase	narrower	same	wider

(f) It was shown in Lab Report 3 that the true mean Twitter stock price was µ = $30.40 with a standard deviation of σ = $12.69. For a random sample of size n = 200, determine the probability (to 4 decimal places) of a type II error occurring in the test in part (a).

Answer 1

B)

p-value = 0.0247

for alpha < 0.0247

sample would have provided evidence against the null hypothesis in part (a)

c)

the 98% confidence interval is 27.927<μ<32.073

d)

yes , since 28 is present in confidence interval

we fail to reject the null hypothesis