Help with number 9 please!asap

Mathematics

1 answer:

andrew-mc [135]3 years ago

7 0

The Associative Property of Multiplication states that the products of a multiplication expression can be grouped within parentheses in any order without changing the value of the expression.
For 4 * 25 * 27,
you can group it like this:
(4 * 25) * 27
= 100 * 27
= 2,700

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A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts. Estimate the true proportion

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Answer: (0.5496, 0.5754)

Step-by-step explanation:

The confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where $\hat{p}$ = Sample proportion , n= sample size , z*= Critical z-value.

Let p be the proportion of all college students who are in favor of banning Hawaiian shirt.

Given, A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts.

i.e. n=4000

$\hat{p}=\dfrac{2250}{4000}=0.5625$

z-value for 90% confidence level is 1.645

Now , 90% confidence interval for p would be :

$0.5625\pm (1.645)(\sqrt{\dfrac{0.5625(1-0.5625)}{4000}})$

$=0.5625\pm (1.645)(\sqrt{0.0000615234375})\\\\=0.5625\pm (1.645)(0.00784368774876)\\\\\approx0.5625\pm0.0129\\\\=(0.5625-0.0129, \ 0.5625+0.0129)\\\\=(0.5496,\ 0.5754)$