Question

1) The average life of light bulbs produced by SABA Electric Co. is expected to be normally distributed with the mean service life of 850 hours and a standard deviation of 100 hours. A random sample of 144 bulbs is tested and it has a mean life of 920 hours. Can it be concluded that the mean service life of the bulbs is more than the expectation at significant level of 0.02? 1) Which method researcher can use to check her idea? a) Hypothesis testing - Z test b) Hypothesis testing - t test c) Sample size estimation for average d) None of the above 2) If she conducts hypothesis testing, she has to consider: a) one-tailed test b) two-tailed test a) one-tailed test because sample size is large b) two-tailed test because sample size is large 3) Which set of ideas can she formulate for her research: H0: µ = 850 and Ha: µ is not equal to 850 H0: µ = 850 and Ha: µ <850 H0: µ = 850 and Ha: µ >850 H0: µ = 920 and Ha: µ <920 H0: µ = 920 and Ha: µ > 920 4) What is the significance level for this test? Level of significance = 100 Level of significance = 20% Level of significance = 20 Level of significance = 85% None of the above 5) What is the computed p-value for this test? 6) Which one of the following is a correct conclusion based on the data given? Use 5% significance level. a) Reject H0. The mean service life of the bulbs is more than the expectation. b) Do not reject H0. The mean service life of the bulbs is more than the expectation. c) Reject H0. The mean service life of the bulbs is not more than the expectation d) Do not reject H0. The mean service life of the bulbs is not more than the expectation e) None of the above. 2) There have been complaints that resident physicians and nurses at the RWJ Hospital desk respond slowly to emergency calls from senior citizens who are medical patients. It is claimed that it takes 10 minutes for non-senior patients. A researcher randomly selected 100 senior citizens and found that on average it took 13 for the selected group of patients to receive proper medical response with the population standard deviation of 3 minutes. At the 0.02 level of significance can it be concluded that response time to emergency calls from senior citizens is longer than the other patients? 1) What are the alternative and null hypotheses? 2) What is the Level of Significance for this test? 3) What is the computed Z value for this test? 4) What is the computed p-value for this test? 5) What is the decision? a) It takes longer for senior citizens to receive medical response. b) It takes almost the same time for senior citizens and non-senior citizens to receive medical response. c) It takes longer for non-senior citizens to receive medical response. d) None of the above. 6) 99% confidence interval is:

Answer 1

1;

Here we have

(1) Since population SD is known and test is about mean so single sample z test should be used.

Correct option :  a) Hypothesis testing - Z test

(2)

Correct option : a) one-tailed test

(3)

H0: µ = 850 and Ha: µ >850

(4)

Level of significance = 0.02

Corret option None of the above

(5)

The test statistics is

Test is right tailed so p-value is:

p-value = P(z > 8.14) = 0.0000

6)

Since p-value is less than 0.05 so we reject the null hypothesis.

a) Reject H0. The mean service life of the bulbs is more than the expectation.