Mathematics, 22.07.2020 18:01 jroy1973

A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some type of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.

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Answer from: shiannlacy33

The interval is 0.7187 < p < 2.421

Step-by-step explanation:

From the question we are told that

The sample size is n = 100

The population proportion is p = 0.81

The confidence level is C = 98%

The level of significance is mathematically evaluated as

$\alpha = 100 -98$

$\alpha = 2%$ %

$\alpha = 0.02$

Here this level of significance represented the left and the right tail

The degree of freedom is evaluated as

df = n-1

substituting value

df = 100 - 1

df = 99

Since we require the critical value of one tail in order to evaluate the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The critical value of $\frac{\alpha}{2}$ and the evaluated degree of freedom is

$t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33$

this is obtained from the critical value table

The standard error is mathematically evaluated as

$SE = \sqrt{\frac{p(1-p )}{n} }$

substituting value

$SE = \sqrt{\frac{0.81(1-0.81 )}{100} }$

SE = 0.0392

The 98% confidence interval is evaluated as

$p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }$

substituting value

0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392

0.7187 < p < 2.421

Answer from: Quest

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh) (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh

Answer from: Quest

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

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