Hypothesis Testing

12 questions

1. 1. Which of the following would not be a typical statement subject to hypothesis testing?
   Trader A generates positive alphaStock X is a good investmentVolatility of Currency N is lower than Currency F
2. 2. In hypothesis testing, a Type 2 error occurs when:
   The null hypothesis is not rejected when the null hypothesis is true. The null hypothesis is rejected when the null hypothesis is true.The null hypothesis is not rejected when the alternative hypothesis is true.

3. 3. Andy Grey believes that the average income of all families in a particular locality is greater than $150,000 per annum. He takes a random sample of 25 houses in the locality and the income of the sample is $155,000.

   The population standard deviation is $20,000. Andy Grey is conducting a hypothesis test at 1% significance level.

   Which of the following correctly represents the null hypothesis?

   Ha: μ > $150,000Ha: μ >= $150,000Ha: μ < $150,000

4. 4. Andy Grey believes that the average income of all families in a particular locality is greater than $150,000 per annum. He takes a random sample of 25 houses in the locality and the income of the sample is $155,000.

   The population standard deviation is $20,000. Andy Grey is conducting a hypothesis test at 1% significance level.

   Calculate the value of the test statistic.

   0.251.251.67

5. 5. Andy Grey believes that the average income of all families in a particular locality is greater than $150,000 per annum. He takes a random sample of 25 houses in the locality and the income of the sample is $155,000.

   The population standard deviation is $20,000. Andy Grey is conducting a hypothesis test at 1% significance level.

   We can say that this is a:

   Left-tailed testRight-tailed testTwo-tailed test

6. 6. Andy Grey believes that the average income of all families in a particular locality is greater than $150,000 per annum. He takes a random sample of 25 houses in the locality and the income of the sample is $155,000.

   The population standard deviation is $20,000. Andy Grey is conducting a hypothesis test at 1% significance level.

   What is the critical value of the z-statistic?

   1.681.962.33

7. 7. Andy Grey believes that the average income of all families in a particular locality is greater than $150,000 per annum. He takes a random sample of 25 houses in the locality and the income of the sample is $155,000.

   The population standard deviation is $20,000. Andy Grey is conducting a hypothesis test at 1% significance level.

   Given 1% significance level, Andy should:

   Fail to reject the null hypothesisReject the null hypothesisCannot make a decision

8. 8. A milk dealer buys 20% fat milk from a milk manufacturer and resells it to consumers. The dealer wants to check and make sure that the milk does not average less than 20% fat. Conduct the hypothesis of the relevant null hypothesis at 5% significance level.

   State the alternative hypothesis.

   Ha: μ > 20%Ha: μ = 20%Ha: μ < 20%

9. 9. A milk dealer buys 20% fat milk from a milk manufacturer and resells it to consumers. The dealer wants to check and make sure that the milk does not average less than 20% fat. Conduct the hypothesis of the relevant null hypothesis at 5% significance level.

   At 5% level of significance, what is the critical value of Z?

   1.64522.33

10. 10. A milk dealer buys 20% fat milk from a milk manufacturer and resells it to consumers. The dealer wants to check and make sure that the milk does not average less than 20% fat. Conduct the hypothesis of the relevant null hypothesis at 5% significance level.

    The dealer draws a random sample of 10 milk packets and finds that the average fat content in the sample is 19.87. Assume we know the population standard deviation is σ = 0.19. Calculate the test statistic.

    -2.1462.146-1.073

11. 11. A milk dealer buys 20% fat milk from a milk manufacturer and resells it to consumers. The dealer wants to check and make sure that the milk does not average less than 20% fat. Conduct the hypothesis of the relevant null hypothesis at 5% significance level.

    Given 5% significance level, the dealer should:

    Fail to reject the null hypothesisReject the null hypothesisCannot make a decision
12. 12. An analyst wants to test the hypothesis that the variance of a normally distributed population is equal to 15. Which of the following is the most appropriate test statistic?
    t-testF-testChi-square test