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3 years ago

The area of a rectangular bathroom mirror is 9 square feet. the mirror is 3 feet wide. how tall is it?

1 answer:

lisabon 2012 [21]3 years ago

5 0

You multpily the length and the width to find the area of a shape. If the square is 3ft wide, then the square is also 3 ft long if the area is 9.
so, how tall is it?
3 ft. I meant rectangle. Its still the same for the height.

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95% confidence interval for the mean time spent studying for the final exam for students taking introductory psychology at this university is [6.85 hours, 7.43 hours].

Step-by-step explanation:

We are given that a sample of 471 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.14 hours and the standard deviation of study times was 3.20 hours.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time spent studying for the exam = 7.14 hours

$\sigma$ = population standard deviation = 3.20 minutes

n = sample of undergraduate students = 471

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $7.14-1.96 \times {\frac{3.20}{\sqrt{471} } }$ , $7.14+1.96 \times {\frac{3.20}{\sqrt{471} } }$ ]

= [6.85 hours , 7.43 hours]

Therefore, 95% confidence interval for the mean time spent studying for the final exam for students taking introductory psychology at this university is [6.85 hours, 7.43 hours].

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