Question

Option 1 or 2

Option 1: Think about a population mean that you may be interested in and propose a confidence interval problem for this parameter. Your data values should be approximately normal. For example, you may want to estimate the population mean number of times that adults go out for dinner each week. Your data could be that you spoke with seven people you know and found that they went out 2, 0, 1, 5, 0, 2, and 3 times last week. You then would choose to calculate a 95% (or another level) confidence interval for the population mean. Assume a random sample was chosen, which is required to determine a confidence interval.

Answer 1

Option 2:

Solution:

Given data:

Number of vehicles sold are SUV' s (n) = 432
Finding number (x) = 142

Now we have to find out the :

calculate a 90% confidence interval for the population proportion:

We already know the formula for the confidence interval for the population proportion, i.e.,

confidence interval for the population proportion CI = $p\wedge \pm (z_{\alpha /2}\ast SE)$

Here we have to find,  $p\wedge$and SE and $z_{\alpha /2}$ values

Formula of $p\wedge$ =  $\frac{x}{n}$

= 142/432

= 0.3264

Now ,SE  = $\sqrt{\frac{P\wedge(1-P\wedge) }{n}}$

=   $\sqrt{\frac{0.3287(1-0.3287) }{432}}$

= $\sqrt{\frac{0.3287(0.6713) }{432}}$

= $\sqrt{\frac{0.22065 }{432}}$

= $\sqrt{0.000510}$

= 0.022583

$\therefore$ SE = 0.022583

We already,know the 90% confidence interval value is 1.645

$\therefore$  $z_{\alpha /2}$ = 1.645

Now, CI =  $p\wedge \pm (z_{\alpha /2}\ast SE)$

= 0.3264  $\pm$ ( 1.645 * 0.022583 )

= 0.3264  $\pm$ ( 0.03714 )

= 0.3264 +0.03714, 0.3264 - 0.03714

CI = ( 0.28926, 0.3635 , )

$\therefore$ 90% confidence interval for the population proportion = ( 0.28926 , 0.3635 )  

• In this given issue the system of developing certainty interim for populace mean by utilizing t-dissemination
• And the strategy of certainty interim for extent by utilizing standard typical circulation is clarified.
• Additionally the precedent issue likewise tackled.

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