Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the expected value of the sample mean speed in a random sample of n = 10 cars?
Q. 2If, in a hypothesis test, the null hypothesis is actually true, which type of mistake can be made?
a. Type 1.
b. Type 2.
c. Type 1 if it's a one-sided test and Type 2 if it's a two-sided test.
d. Type 2 if it's a one-sided test and Type 1 if it's a two-sided test.
Q. 3Items produced by a certain process are supposed to weigh 90 grams. However, the process is such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights is normal with a mean of 89.8 grams and a standard deviation of 1.1 gram. If we have a random sample of 10 of these items, what is the probability that their average weight exceeds 91 grams?
Q. 4In a hypothesis test the decision was made to not reject the null hypothesis. Which type of mistake could have been made?
a. Type 1.
b. Type 2.
c. Type 1 if it's a one-sided test and Type 2 if it's a two-sided test.
d. Type 2 if it's a one-sided test and Type 1 if it's a two-sided test.
Q. 5Items produced by a certain process are supposed to weigh 90 grams. However, the process is such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights is normal with a mean of 89.8 grams and a standard deviation of 1.1 gram. Suppose we have a random sample of 2 of these items. What is the probability that both these items weigh more than 91 grams?
Q. 6In hypothesis testing, a Type 2 error occurs when
a. the null hypothesis is not rejected when the null hypothesis is true.
b. the null hypothesis is rejected when the null hypothesis is true.
c. the null hypothesis is not rejected when the alternative hypothesis is true.
d. the null hypothesis is rejected when the alternative hypothesis is true.
Q. 7Items produced by a certain process are supposed to weigh 90 grams. However, the process is such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights is normal with a mean of 89.8 grams and a standard deviation of 1.1 gram. Suppose we sample one of these items. What is the probability that it weighs more than 91 grams?
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