Question

In: Math

For the following data values below, construct a 98% confidence interval if the sample mean is...

For the following data values below, construct a 98% confidence interval if the sample mean is known to be 9.808 and the population standard deviation is 5.013. (Round to the nearest thousandth) (Type your answer in using parentheses!Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78)

6.6, 2.2, 18.5, 7.0, 13.7, 5.4, 5.3, 5.9, 4.7, 14.5

2.0, 14.8, 8.1, 18.6, 4.5, 17.7, 15.9, 15.1, 8.6, 5.2

15.3, 5.6, 10.0, 8.2, 8.3, 9.9, 13.7, 8.5, 8.2, 7.9

17.2, 6.1, 13.7, 5.7, 6.0, 17.3, 4.2, 14.7, 15.2, 3.3

3.2, 9.1, 8.0, 18.9, 14.2, 5.1, 5.7, 16.4, 10.1, 6.4

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 9.808

Population standard deviation = = 5.013

Sample size = n =50

At 98% confidence level the z is ,l

= 1 - 98%

= 1 - 0.98 =0.02

/2 = 0.01

Z/2 = Z_{0.01= 2.326}

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 2.326 * (5.013 / $\sqrt$ 50)

= 1.65

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

- E < < + E

9.808 - 1.65 <   <9.808 + 1.65

8.158 <   < 11.458

( 8.158 ,  11.458 )

milcah answered 4 months ago

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