Question

page 1 M155/Beebe/S19 TEST 3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5 POINTS APIECE. (Circle answers.) For problems 1 and 2, do one of the following, as appropriate, to calculate a confidence interval for the given confidence level: (a) find the critical value za/2. (b) find the critical value ta/2, or (c) state that neither the normal or t distribution applies. PROBLEM 1 . Confidence level 91%; n-45; ơ is known; population appears to be very skewed. za/,-1.70 D) A) ta/2 = 1.34 B) t"/2-1, 645 E) Neither normal nor t Za/2-1.75 C) PROBLEM 2, Confidence level 98%; n = 7; σ is unknown; population appears to be normally distributed. A) ta/2 -1.96 B) a/-2.998 C) za/2 2.05 D) za/2 2.33 E) Neither normal nor t PROBLEM 3, A 90% confidence interval for the height of adult women in the US, from a sample of n 50 women, has a margin of error of 4 in. Would the margin of error of a 95% confidence interval for a sample of the same size be: (C) Equal to 4, (D) Impossible to tell (B) Smaller than 4, (A) Larger than 4, PROBLEM 4, A 90% confidence interval for the height of adult women in the US. from a sample of n 50 women, has a margin of error of 4 in. Would the margin of error of a 90% confidence interval for a sarmple of size n-25 be: (D) Impossible to tell (C) Equal to 4, (B) Smaller than 4, (A) Larger than 4,

Answer 1

P1) Since population standard deviation is given and sample size is 45>30

So using Central limiting theorem we can use normal distribution for the distribution of means.

Also from normal table we see that $z_{\alpha/2}$=1.70

Option D is correct

P2) Since sample size is small and population standard deviation is not given and population is normally distributed so we use t test

So t value is =2.988

to/2

Option B is correct

P3) As with increase in confidence level the critical value also increases so does margin of error.

Hence with increase in confidence level from 90% to 95% the margin of error will be larger than 4

Option A is correct

P4) The margin of error is inversely proportional to sample size. So as sample size decreases Margin of error increase

So for 25 sample margin of error will be larger than 4

Option A is correct