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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2013-10-08 06:22:28

A t - table is the students distribution. That is for small sample sizes.

cynthia258
2013-10-08 06:19:38

In part c,

the confidence interval is 97.5%. Then, which t-table should I look at? The 95% one or the 98% one? Sorry for disturbing and thank you again.

bobbym
2013-10-08 05:43:36

Hi;

For one thing (15 - 19.5 )  /  2.612 ≈ -1.7228

The rest could be just round off. Please recompute with the correct z score I gave above.

cynthia258
2013-10-08 04:46:43

p(x<15)=p(z<  15-19.5  /  2.612  )=p(z<-1.7225)=0.5-0.4573=0.0427

why isn't my ans same with yours? is my calculation anything wrong?

bobbym
2013-10-07 22:57:37

Hi;

n = 30 is what I picked.

This guy explains it well.

http://www.jedcampbell.com/?p=262

Also it is the magic number for picking from any distribution.

cynthia258
2013-10-07 22:36:00

excuse me, how can you know p(x<15) in part b? i don't understand why the number is 15

bobbym
2013-10-04 04:13:21

Hi cynthia258;

Welcome to the forum!

a) They usually say n = 30 or more. This is only a very rough estimate and their are precise bounds but n = 30 is what we will use.

mean = .65 x 30.

The standard deviation is



b) P(15 or less agree) = .04248

cynthia258
2013-10-04 03:03:47

A statistician conducted a research and the results showed that 65% of blue-collar workers agree that 8 working hours per  day is acceptable. A random sample of n blue-collar workers was selected and let X be a random variable defined as the number of blue-collar workers agree the view.

(a)What is the minimum value of n such that X can be approximated by the normal random variable? Using this value of n,find the mean and standard deviation of the sampling distribution of the sample proportion.

(b) Based on the results of (a), find the probability that less than half of the blue-collar workers agree the view.


(c) A statistician conducted the same research for a random sample of 200 white-collar workers. It was found that 150 of them agree the view. Find the 97.5% confidence interval for the population proportion of white-collar workers who agree that 8 working hours per day is acceptable.



Thank you.smile

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