Q1. Assuming that the data are normally distributed with a mean of 25 and a standard deviation of 1.25, what is the z-score for a value of 27?
Q2. The mean hours of Internet usage by adults in the US in claimed to be 25 hours per week. A hypothesis test is performed at a level of significance of 0.05 with a P-value of 0.08. Choose the best interpretation of the hypothesis test.
- Reject the null hypothesis; there is enough evidence to reject the claim that the mean of hours Internet usage by adults in the US is 25 hours per week.
- Reject the null hypothesis; there is enough evidence to support the claim that the mean hours Internet usage by adults in the US is 25 hours per week.
- Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean hours of Internet usage by adults in the US is 25 hours per week.
- Fail to reject the null hypothesis; there is not enough evidence to support the claim that the mean hours of Internet usage by adults in the US is 25 hours per week.
Q3. In a hypothesis test conducted at a level of significance of 2%, a P-value of 0.035 was obtained. Choose the best interpretation of the hypothesis test.
- Fail to reject the null hypothesis; there is not enough evidence to reject the claim that 22% of students fail the entry level exam.
- Fail to reject the null hypothesis; there is not enough evidence to support the claim that 22% of students fail the entry level exam.
- Reject the null hypothesis; there is enough evidence to reject the claim that 22% of students fail the entry level exam.
- Reject the null hypothesis; there is enough evidence to support the claim that 22% of students fail the entry level exam.
Q4. You want to buy light bulbs and you want to choose between two vendors. Vendor A's light bulbs have a mean life time of 800 hours and a standard deviation of 175 hours. Vendor B's light bulbs also have a mean life time of 800 hours, but a standard deviation of 225 hours. You want light bulbs that have more life time consistency, which vendor will you purchase from?
- Vendor A because you will be more likely get light bulbs with the same life time
- Vendor B because you will be more likely get light bulbs with the same life time
- Either one because both produce light bulbs with the same mean life time.
- Neither one because a mean height of 800 inches is too short for a light bulb.
Q5. A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 45% red, 35% blue, 15% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $5, $15, $25, $60 for red, blue, yellow and green ball respectively.
Winning amount 5 15 25 60
Probability 45% 35% 15% 5%
- The expected winning amount is $28.50
- The expected winning amount is $14.25
- The expected winning amount is $25.50
- The expected winning amount is $11.25