TUTORIAL 4
1) A study was carried out to estimate the average life of a large shipment of light bulbs. Previous studies indicated that the standard deviation is known to be 100 hours. A random sample of 50 light bulbs was selected and indicated that the sample average life was 350 hours. Construct a 95% confident interval estimate of the true average life for light bulbs in this shipment.
2) The brightness of a television picture tube can be evaluated by measuring the amount of current required to achieve a particular brightness level. A random sample of 10 tubes indicated a sample mean is 317.2 microamps and a sample standard deviation is 15.7 microamps. Find (in microamps) a 99% confidence interval estimate for mean current required to achieve a particular brightness level.
3) 18 male undergraduate students and 20 female undergraduate students are randomly selected from faculty of mechanical engineering. Result for their test are shown below:
Male / /Female / /
Assume that both populations are normally distributed and have equal population variances. Construct a 95% confident interval for the difference in the two means.
4) Two candidates A and B will compete for the post of President of Pulai Golf Club. From 100 members of the club, 57 prefer voting for A as the president. Construct a 94% confidence interval for the population of all voters who favour candidate A. What can they assert with 97% confident about the maximum error of their estimate?
5) The diameter of a two years old Sentang tree is normally distributed with a standard deviation of 8 cm. How many trees should be sampled if it is required to estimate the mean diameter within 15 cm with 95% confidence interval?
6) Two separate surveys were carried out to investigate whether or not the user of Plus highway were in favour of raising the speed limit on highways. From the 250 car drivers interviewed, 220 were in favour of raising the speed limit while from the 200 motorist interviewed, 180 were in favour.
i) Find a 95% confident interval for the difference in proportion between the car drivers and motorist who are in favour of raising the speed limit.
ii) Test hypothesis for the difference between car drivers and motorist who were in favour of raising the speed limit on highways at 1% significance level.
7) A teacher claims that students in Class A put in more hours studying compared to other students. The mean numbers of hours spent studying per week is 25 hours with a standard deviation of 3 hours per week. A sample of 27 Class A students was selected at random and the mean number of hours spent studying per week was found to be 26 hours. Can the teacher’s claim be accepted at 5% significance level?
8) Aisyah makes “kerepek ubi” and sell them in packets of 100g. 12 randomly selected packets of “kerepek ubi” are taken and their weights in g are recorded as follows:
98 / 102 / 98 / 100 / 96 / 9197 / 97 / 100 / 94 / 101 / 97
Perform the required hypothesis test at 5% significance level to check wheter the mean weight per packet of “kerepek ubi” is not equal to 100g.
9) An experiment is done to test strength of two types of glasses. A sample of 12 pieces of glasses has a mean strength of 40 kg and a standard deviation of 2 kg. A sample of 13 pieces of glasses has a mean strength of 38 kg and a standard deviation of 2.5 kg. test at 5% significance level that the mean strength of the two types of glasses is the same. Assume the two population variances are equal.
10) A manufacturer of a detergent claimed that his detergent is 95% effective in removing tough stains. In a sample of 300 people who had used the detergent, 279 people claimed that they were satisfied with the result. Determine whether the manufacturer’s claim is true at 1% significance level.
11) The management of Priority Health Club claims that its members lose an average of 10 pounds or more within the first month after joining the club. A consumer agency that wanted to check this claim took a random sample of 36 members of this health club and found that they lost an average of 9.2 pounds within the first month of membership with a standard deviation of 2.4 pounds. Find the p-value for this test. What will your conclusion be if What if
12) At Canon Food Corporation, it took an average of 50 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 50 minutes. A sample of 40 workers showed that it took, on average, 47 minutes for them to learn the food processing procedure on the new machine with a standard deviation of 7 minutes. Find the p-value for the test that the mean learning time for the food processing procedure on the new machine is different from 50 minutes. What will your conclusion be if
Answers
1. (322.28, 377.72)
2. (304.42, 329.98)
3. (1.46, 10.54)
4. (0.4769,0.6631), E = 0.107
5. 109
6. i) (-0.078, 0.038) ii) -0.674
7. 1.732
8. -2.737
9. 2.196
10. -1.5894
11. P-value = 0.0228
12. P-value = 0.0068