EQuestion Help 00 8.2 RA-1 ae Fill in the blanks to complete the following state

Question

EQuestion Help 00 8.2 RA-1 ae Fill in the blanks to complete the following statements. sall (a) For the shape of the distribution of the sample proportion to be approximately normal, itis required that npl1-p)2 (b) Suppose the proportion of a population that has a certain characteristic is 0.66. The mean of the sampling distribution of p from this population is This is a reading assessment question. Becertain of your answer because you only getone attempt on this queston.) e Repo (a) For the shape of the distribution of the sample proportion to be approximately normal, required that np(1- p)2 tis dom (ype an integer or a decimal.) dom arning dom

Explanation / Answer

Question 8.2 RA -1 (a) For the shape of the distribution of the sample proportion to be approximately normal , it is required that

np(1-p) > = 10 [ This is called rule of thumb so can't be explained]

simlarly np>=10 and n(1-p)>=10

(b) proportion = 0.65

the mean of the sampling distribution of p^ from this population is mup = 0.65

Question 8.2 21 -T

Here out of 400, 208 voted for referendum in the given sample so p = 208/400 = 0.52

p0 = 0.49

Null HYpothesis : p = 0.49

ALternative Hypothesis : p 0.49

Test Staitistic:

Z= ( p - p0)/ sqrt [ p0 (1- p0)/n] = ( 0.52 - 0.49] / sqrt[ 0.49 *0.51/ 400]

= 0.03/ 0.025 = 1.2

Zcritical = 1.96 for significance level alpha = 0.05

so we cannot reject the null hypothesis and conculde that the given sample proportions is as same as population result where 0.49 % voters voted for referendum.

(b) The probability that more than 208 out of 400 voted for referendum = p - value calculating from Z - table for z = 1.2

P( X>= 208) = 1 - 0.8849 = 0.1151 { where 0.8849 is the respective p - value for Z = + 1.2

Question 8 .2 18- I

p 9 not habving credit card) = 0.37

sample size = 900

(a) let say p^ is the proportion of people who doesn't have credit card out of sample .

Option c is correct as approximately normal because n <= 0.05 N and np(1- p) >= 10

where N = adult population which will be in billions

n = 900

p = 0.37

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