Test of Means and Proportions 1.)The proportion of families buying milk from company A in a certain city is believed to be p = 0.6. If a random sample of 10 families shows that 3 or less buy milk from company A, we shall reject the hypothesis that p = 0.6 in favor of the alternative p < 0.6. a. Find the probability of committing a type I error if the proportion is p = 0.6. b. Find the probability of committing a type II error if the proportion is p = 0.4. 2.) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Test the hypothesis that μ = 800 hours against the alternative that μ ≠ 800 hours is a random sample of 30 bulbs has an average life of 788 hours. Use a 0.04 level of significance 3.) The average height of females in the freshman class of a certain college has been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there a reason to believe that there has been a change in the average height if a random sample of 50 females in the resent freshman class has an average height of 165.2 centimeters? Use a 0.02 level of significance. 4.) A manufacturer claims that the average tensile strength of thread a exceeds the average tensile strength of thread B by at least 12 kilograms. To test this claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread has an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms and a standard deviation of 5.61 kilograms. Test the manufacturer’s claim using a 0.05 level of significance. 5. At a certain college it is estimated that fewer than 25% of the students have cars on campus. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to have cars> use a 0.05 level of significance.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Test of Means and Proportions
1.)The proportion of families buying milk from company A in a certain city is believed to be p = 0.6. If a random sample of 10 families shows that 3 or less buy milk from company A, we shall reject the hypothesis that p = 0.6 in favor of the alternative p < 0.6.
a. Find the
b. Find the probability of committing a type II error if the proportion is p = 0.4.
2.) An electrical firm manufactures light bulbs that have a length of life that is approximately
3.) The average height of females in the freshman class of a certain college has been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there a reason to believe that there has been a change in the average height if a random sample of 50 females in the resent freshman class has an average height of 165.2 centimeters? Use a 0.02 level of significance.
4.) A manufacturer claims that the average tensile strength of thread a exceeds the average tensile strength of thread B by at least 12 kilograms. To test this claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread has an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms and a standard deviation of 5.61 kilograms. Test the manufacturer’s claim using a 0.05 level of significance.
5. At a certain college it is estimated that fewer than 25% of the students have cars on campus. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to have cars> use a 0.05 level of significance.
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