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The mathematical scores of 6 groups of 4 students each are shown below. Test whether the differences in scores may be attributed to chance, at .01 significance level.
Group 1: Student1 84, Student2 88, Student3 70, Student4 80. Group 2: Student1 90, Student2 95, Student3 93, Student4 80. Group 3: Student1 70, Student2 73, Student3 85, Student4 90. Group 4: Student1 95, Student2 96, Student3 90, Student4 90. Group 6: Student1 85, Student2 78, Student3 75, Student4 90. Group 6: Student1 93, Student2 85, Student3 80, Student4 90.
A normal population with unknown variance is believed to have a mean of 20. Is on likely a random sample of size 9 from this population that has mean 24 and standard deviation of 4.1. If not, what conclusion would you draw
Below are the bowling scores of 4 groups of 4 players each. At 5% significance level, find out if there is unusual variation among the four groups. Group A: Player A 98, Player B 78, Player C 95, Player D 110. Group B: Player A 100, Player B 95. Player C 90, Player D 102 Player D 85. Group C: Player A 87, Player B 95, Player C 105, Player D 88 and Group D: Player A 90, Player B 93, Player C 95, Player D 97.
Two methods of teaching statistics are being tried by a professor. A class of 40 students is taught by method A and a class of 36 is taught by method B. The two classes are given the same final examination. The scores are x̄1=78, x̄2 =74. Using a .01 significance level, can we conclude that the average final examination scores produced by the two methods are different if the population standard deviation is 5?
A company which sells biscuits claims “Contents 880 grams” on the package. A sample of 28 packages yields an average of 800 grams. From past experience, the population standard deviation has been 50 grams. Using a .05 significance level, what conclusions would be drawn concerning the standard which the company is trying to achieve?
A fisherman decides that he needs a line that will weight 5 kilos if he is to catch the size of the fish he desires. He tests 14 pieces of Brand P line and finds a sample mean of 5.6 kilos. If it is known that σ= .4 kilos, what can he conclude about brand P?
Incoming freshmen are given entrance examinations in a number of fields, including English. Over a period of years, it has been found that the average score in English examination is 80 with a standard deviation of 7.8. An English instructor examines the scores for his class of 30 and finds that their average is 85. Can the instructor claim that the average score has increased?
A sample survey on the average total yearly expenditure included 150 students of a certain university. The mean total expenditure per student per year for the sample was 3,000 with a standard deviation of 500. How likely is it that the students spend an average of 3500 per year as claimed by a parent at .01 significant level.
A sample survey on the average total yearly expenditure included 150 students of a certain university. The mean total expenditure per student per year for the sample was 3,000 with a standard deviation of 500. How likely is it that the students spend an average of 3500 per year as claimed by a parent at .01 significant level.
A dry-cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 29 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject the null hypothesis that p = 0.7; otherwise, we conclude that p > 0.7
(i) Evaluate α , assuming that p = 0.7(ii) Evaluate β for the alternative p = 0.8
