Statistics and Probability Answers

using continuity correction probability of observing less than 10 successes answer?

Cans of black olives are filled by two machines (A and B) in a food processing factory. The distribution of the gross mass is known to be normal with mean 500 g and standard deviation 5.3 g for machine A, and normal with mean 504 g and standard deviation 4.8 g for machine B. A batch of canned black olives have been filled by the same machine, but it is not known which machine was used. As some substandard olives have accidently been used by machine A, it is decided to test

H0: batch is from machine A, against

H1: batch is from machine B

By weighing a random sample of 6 cans and rejecting H0 if the mean mass exceeds a predetermined mass of k g.

It is decided to increase the sample size before reaching a final conclusion. Determine how many more cans are needed to be weighed if the risk of type I error is to remain at 5%, but the risk of type II error is to be reduced to just under 1%?

A medicine manufacturing company is trying to choose between two pharmaceutical companies that are competing in the market. First Company has offered the manufacturing company Rs 10,000 plus Rs 2 per medicine sold. Second Company has offered the manufacturer Rs 2,000 plus Rs 4 per medicine sold. The manufacturer believes that five levels of demand are as follows: 1,000, 2,000, 5,000, 10,000 and 50,000. Compute the payoffs for each level of demand for first company and second company. Construct a payoff Table, indicating the events and alternative courses of action. Construct a decision tree. Construct an opportunity loss Table

Following data gives the weights of 40 students at a university.

138 164 150 132 144 125 149 157 146 158 140 147 136

148 152 144 168 126 138 176 163 119 154 165 156 173

142 147 135 153 140 135 161 145 135 142 150 156 145

128

Tabulate the data into frequency distribution taking 9 as interval. Also construct histogram, 

frequency polygon and ogive.

An insurance company rounds 50000 insurance premiums to the nearest dollar. Assuming that the fractional parts of the premiums are continuous and uniformly distributed between 0 and 1, compute the probability that the total amount owing will be altered by more than $60.

You may use R to assist you in answering this question, but you would need to list out all working details.

(15 marks)

Professor Albert Francis had students in his Psychology 201 class rate his performance. The ratings are kept from the professor till release of the course marks. The course marks are shown in the table below, under the respective rating given by the students.

Performance Rating

Excellent Good Fair Poor

94 75 70 68 90 68 73 70 85 77 76 72 80 83 78 65

88 80 74 68 65

65

Table Q5

Apply and perform an appropriate test to check if there is a difference in the mean marks received by students in each of the rating categories. Show all relevant workings and steps in

                   the test, and test at 1% level of significance.

(20 marks)

WCans of black olives are filled by two machines (A and B) in a food processing factory. The distribution of the gross mass is known to be normal with mean 500 g and standard deviation 5.3 g for machine A, and normal with mean 504 g and standard deviation 4.8 g for machine B.

A batch of canned black olives have been filled by the same machine, but it is not known which machine was used. As some substandard olives have accidently been used by machine A, it is decided to test

H0: batch is from machine A, against H1: batch is from machine B

By weighing a random sample of 6 cans and rejecting H0 if the mean mass exceeds a pre- determined mass of k g.

(a) Determine constant k such that the risk of type I error is 5%. What is the corresponding

risk of type II error?

(b) Apply and carry out the test for a sample of 6 cans with masses 511, 499, 500, 498, 507,

495 g.

A new drug cures 9 of 200 patients suffering from a type of cancer, for which the historical cure rate is 2%. Perform a test to check on the significance of this result, at both 5% and 1% levels of significance. Based on your conclusion, comments on the efficacy of the treatment using this new drug.

(15 marks

Men’s heights are normally distributed with mean 180 cm and standard deviation 4 cm, while women’s heights are normally distributed with mean 175 cm and standard deviation 3 cm. In a sample of 100 married couples, the average difference between husband’s height and wife’s height is 3.4 cm. By performing an appropriate test, comment on if the choice of partner in marriage is influenced by considerations of height, at 1% level of significance. Show full working details for your test.

(15 marks)

Pascal Co. is considering replacing one of its software with a new software. Before a final decision is made, Pascal Co. has taken a sample of four hundred customers. After surveying the customers, 250 recommended that they would purchase the new software. Estimate the value of the population proportion. Develop a 99 percent confidence interval for the population proportion. Interpret your findings.