Question

In: Statistics and Probability

12. Big Shark, a bicycle shop, promises to repair cycles within 3 days. A 96% confidence...

12. Big Shark, a bicycle shop, promises to repair cycles within 3 days. A 96% confidence interval for the proportion of all cycles that are repaired in time is 88% ± 6%. What does this mean?

a. Between 82% and 94% of all cycles are repaired in time.

b. Between 82% and 94% of all cycles are repaired in time, 96% of the times.

c. 96% of all random samples (of same size) will show that between 82% and 94% of all cycles are repaired in time.

d. At least 96% of all samples (of same size) will have a 96%-confidence interval that will contains the true proportion of cycles that will be repaired in time, (82%, 94%) is just one such interval

?

14. A certain null hypothesis is rejected at 2% level of significance. If the level of significance is increased to 5%, the power of the test increases.

a. True

b. False

Expert Solution

12. A 96% confidence interval means that 96% of all random samples of the same size will have a 96% -confidence interval that will contain the true proportion of cycles that will be repaired in time. (82%, 94%) is just one such interval.

Option d is correct.

14. If the significance level increases, the probability of rejecting the null hypothesis increases.

The power of a test is called the probability of rejecting a null hypothesis when it is not true.

Hence, if a null hypothesis is not true, and if we have a higher significance level then there is a higher probability of rejecting the null hypothesis, which in turn increases the power of the test.

Hence, the statement is true.

option 'a' is correct.

orchestra answered 1 year ago

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