Homework SourseDetermine and whether the following statements are True or F
Determine and whether the following statements are True or False and explain why. If false, turn the statement into a true one by changing (adding or removing) as few words as possible. Explain why the change turns the statement into a true one.
a) As the sample size increases the probability of a type I error and the probability of a type II error decreases when testing a null hypothesis at the 5% level.
b) The central limit theorem states that the sampling distribution of the mean is normal.
c) If X ~ N(m,s2) if and only if Z=(X-m)/s ~N(0,1)
d) Only a table of the N(0,1) is needed because any probabilities orpercentiles relating to other normal distributions can be obtained from it.
e) The estimated standard error of the mean decreases as the sample size increases.
f) The sample variance can be made into an unbiased estimate of the population variance by multiplying it by N/(N-1).
Solution
As the sample size increases the probability of a type I error and the probability of a type II error increases when testing a null hypothesis at the 5% level. The larger the sample size, the test is more likely to detect small difference. The central limit theorem states that the sampling distribution of the mean is normal. TRUE. If X ~ N(m,s2) then the standardized for of X that is Z=(X-m)/s ~N(0,1). Only a table of the N(0,1) is needed because any probabilities or percentiles relating to other normal distributions can be obtained from it. TRUE The estimated standard error of the mean decreases as the sample size increases. TRUE. The sample variance can be made into an unbiased estimate of the population variance by multiplying it by N/(N-1). TRUE.
