A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.42 deciliters. Find a 95% confidence interval for the mean of all drinks dispensed by this machine if random sample of 36 drinks had an average content of 22.19 deciliters.
Q.4: A soft-drink machine is regulated so that the amount of drink dispensed is approximately
Q.5: The heights of a random sample of 50 college students showed a mean of 173.78 centimeters and a standard deviation of 7.5 centimeters.
a) Construct a 95% confidence interval for the mean height of all college students.
Q.6: A random sample of 100 automobile owners shows that an automobile is driven on average 23198.22 kilometers per year, in the state of Virginia, with a standard deviation of 3997.62 kilometers.
a) Construct a 95% confidence interval for the average number of miles an automobile is driven annually in Virginia.
Q.10: Regular consumption of presweetened cereals contribute to tooth decay, heart disease and other degenerative diseases, according to studies by Dr. W.H.Bowen of the National Institute of Health and Dr. J Yubden, professor of Nutrition and Diabetics at the University of London. In a random sample of 20 similar simple servings of Alpha-Bits, the average sugar content was 10.471 grams with a standard deviation of 2.519 grams. Assuming that the sugar contents are normally distributed, construct a 95% confidence interval for the mean sugar content for single servings at Alpha-Bits.
Q.11: The contents of 20 similar containers of a commercial soap are normally distributed with mean 9.975 liters and standard deviation is 0.2571 liters. Find a 95% confidence interval for the mean soap content of all such containers.
Q.12: A random sample of 20 cigarettes of a certain brand has an average nicotine content of 8.502 milligrams and a standard deviation of 6.079 milligrams. Construct a 95% confidence interval for the true average nicotine content of this particular brand of cigarettes, assuming an approximately normal distribution.
Q.13: A random sample of 20 female students in a certain dormitory showed an average weekly expenditure of $10.306 for snack foods with a standard deviation of 5.49. Construct a 95% confidence interval for the average amount spent each week on snack food by female students living in the dormitory, assuming the expenditures assuming to be approximately normally distributed.
Q.14: A random sample of n1=24 taken from a normal population with a standard deviation = 5.65 has a mean of x1=79.96. A second random
Q.15: Two kinds of threads are been compared for strength. Fifty pieces of each type of thread are tested under similar conditions. Brand A has an average tensile strength of 79.72 kg with a standard deviation of 5.14 KG while Brand B has an average tensile strength of 86.89 with a standard deviation of 5.63. Construct a 95% confidence interval for the difference of the population means.
Q.16: A study was made to estimate the difference in salaries of college professors in the private and state college of Virginia. A random sample of 100 professors in private colleges showed an average 9months salary of 25050.55 with a standard deviation of 1098.62. A random sample of 200 professors in state colleges showed an average salary of 26006.71 with a standard deviation of 1362.17. Find a 95% confidence interval for the difference of between the average salaries of professors teaching in state and private college of Virginia.
Q.17: Given two random samples of size n1= 9, and n2=16, from two independent normal populations with x1=63.05, s1=5.984and x2=58.94, s2=4.9. Find 95% confidence interval for the difference between two means.
Q.18: Students may choose between a 3 semester hour course in physics without labs and a 4 semester hour course with labs. If 12 students in the section with labs made an average examination grade of 83.89 with a standard deviation of 3.63 and 18 students in the section without labs made an average grade of 76.3 with a standard deviation of 5.71. Find a 95% confidence interval for the difference between the average grades for two courses. Assume the population to be approximately normally distributed with equal variances.
Q.19: A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands and experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are
Sample mean Sample standard deviation
Brand A 36946.28km 4541.5km
Brand B 37855.84km 4033.59km
Compare a 95% confidence interval for the difference between the two means assuming the population to be approximately normally distributed .
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