In: Statistics and Probability

Calculate the margin of error and construct the confidence interval for the population mean using the Student's t-distribution (you may assume the population data is normally distributed).

T-Distribution Table

**a.** x̄ =87.3, n=64, s=19.6, x̄ =87.3,
n=64, s=19.6, 98% confidence

E=E=

Round to two decimal places

< μ < < μ <

Round to two decimal places

**b.** x̄ =31.6, n=44, s=14.6, x̄ =31.6,
n=44, s=14.6, 90% confidence

E=E=

Round to two decimal places

< μ < < μ <

Round to two decimal places

Please provide correct answers. thanks

Solution :

a) degrees of freedom = n - 1 = 64 - 1 = 63

t/2,df = t0.01,63 = 2.387

Margin of error = E = t/2,df * (s /n)

= 2.387 * ( 19.6 / 64)

Margin of error = E = 5.85

The 98% confidence interval estimate of the population mean is,

- E < < + E

87.3 - 5.85 < < 87.3 + 5.85

( 81.45 < < 93.15 )

b) degrees of freedom = n - 1 = 44 - 1 = 43

t/2,df = t0.05,43 = 1.681

Margin of error = E = t/2,df * (s /n)

= 1.681 * ( 14.6 / 44)

Margin of error = E = 3.70

The 90% confidence interval estimate of the population mean is,

- E < < + E

31.6 - 3.70 < < 31.6 + 3.70

( 27.90 < < 35.30 )

Calculate the margin of error and construct a confidence
interval for the population proportion using the normal
approximation to the p̂ p̂ -distribution (if
it is appropriate to do so).
Standard Normal Distribution Table
a. p̂ =0.9, n=160, α =0.2
p̂ =0.9, n=160, α =0.2
E=E=
Round to four decimal places
Enter 0 if normal approximation cannot be used
< p < < p <
Round to four decimal places
Enter 0 if normal approximation cannot be used
b. p̂ =0.45, n=140, α
=0.2 p̂ =0.45, n=140, α =0.2...

Match the margin of error for an 80% confidence interval to
estimate the population mean with sigma σ equals=50
with its corresponding sample sizes.
Question 5 options:
a.) 8.07. 1.) n= 34
b.) 9.45 2.) n= 46
c.) 10.99 3.) n= 63

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estimate the population mean with nequals24 and s = 13.5 for the
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91%
95%
98%

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a. 80%
b.90%
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repeat for 90% and 99%

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Determine the margin of error for a 99% confidence interval to
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Determine the margin of error for a confidence interval to
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a. The margin of error for a confidence interval to estimate the
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