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To test the hypothesis that a coin is fair, the following decision rules are adopted: (1) Accept the hypothesis if the number of heads in a single sample of 100 tosses is between 40 and 60 inclusive, (2) reject the hypothesis otherwise. a. Find the probability of rejecting the hypothesis when it is actually correct. b. Interpret graphically the decision rule and the result of part (a). c. What conclusions would you draw if the sample of 100 tosses yielded 53 heads? 60 heads?
An examination was given to two classes consisting of 40 and 50 students, respectively. In the first class the mean grade was 74 with a standard deviation of 8, while in the second class the mean grade was 78 with a standard deviation of 7. Is there a significant difference between the performance of the two classesat a level of significance of a. 0.05, b. 0.01? c. What is the P value of the test
The following data represent the prices (in rand) of seven vehicles at a dealer:
210 125; 188 623; 375 016; 214 700; 132 210; 235 910; 198 410
The mean price of these vehicles is R222 142. Now leave out the most expensive vehicle (with a price of
R375 016) and calculate the mean price for the remaining vehicles. The amount by which the mean price
per vehicle drops after the most expensive vehicle was removed, rounded to the nearest rand, is
Let Y = |Z|, where Z ∼ N (0, 1) be a discrete random variable with the following PMF: (i) Find E(Y ) and V ar(Y ). (ii) Find V ar(Y ). (iii) Find the CDF and PDF of Y .
The data set given below consists of six pairs of (x, y); (10, 70); (12, 65); (2, 96); (0, 94); (8, 75); (5, 82) I Based on a plot, determine whether the relationship between x and y is linear or not. a. b. Find the value of r to analyze the strength of the relationship.
The appropriate form of the test-statistics in conducting hypothesis testing about the population proportion when the Central Limit Theorem is to be used is t-test.
If P = 13%, x = 45, n = 250, then the computed z value is 2.351
1) An athlete is running in 5 races and in each race he has a 70% chance of winning. what is the probability that he will win at least two races?
2) the average number of cars arriving at a particular red light each day is 4. Assuming a poison distribution, calculate the probability that on a given day, less than three cars will arrive at the red light.
An athlete is running in five races and in each race he has a 70% chance of winning. What is the probability that he will win at least two races?
The critical value or t-value of a one-tailed test when n=18 for 95% of confidence interval is 1.734 *
