Question

just explain in words

1. Suppose you are drawing a random sample of size n > 0 from n(μ, σ2) where σ 0 is known. Decide if the following statements are true or false and explain your reasoning. Assume our 95% confidence procedure is X - 1.96, X +1.96 小2 Vn a. If (3.2.5.1) is a 95% CI from a particular random sample, then there is a 95% chance that μ is in this interval. b. If (32.5.1) is a 95% CI from a particular random sample, then there is a 95% chance that the mean from our next random sample will be in this interval. C. A 95% CI will contain 95% of the possible values from the population we are studying. d. If we generate 400 random Cls using our 95% confidence procedure, we expect about 20 intervals to not contain μ.

Answer 1

a) True
since given interval (3.2, 5.1)
95% chance that the population mean value is lies between 3.2 and 5.1

b) False
since given interval (3.2, 5.1)
95% chance that the population mean value is lies between 3.2 and 5.1

c) False
since given interval (3.2, 5.1)
95% chance that the population mean value is lies between 3.2 and 5.1

d) TRUE
since 95% chance that the population mean value is lies between 3.2 and 5.1 means 5% chance the population mean would be outside the limits.

we have 400 samples so approximately 20 samples are outside the limits