Question

1. Suppose we know that the population standard deviation for SAT scores (σ) is 300. Provide each of the following using this information.

1. A random sample of n = 90 results in a sample mean of 1050. Provide a 95% confidence interval estimate of µ. What is the value for the margin of error? Interpret your results.
2. A random sample of n = 2500 results in a sample mean of 1050. Provide a 95% confidence interval estimate of µ.
3. A random sample of n = 90 results in a sample mean of 1050. Provide a 99% confidence interval estimate of µ.

Answer 1

given data are:-

population sd () = 300

a). sample size (n) = 90

sample mean () = 1050

z critical value for 95% confidence level, both sided test be:-

margin of error :-

95% confidence interval estimate of µ be:-

= (988.02 , 1111.98 )

interpretation:-

we are 95 % confident that our population mean score µ will lie within 988.02 and 1111.98

b).

sample size (n) = 2500

sample mean () = 1050

z critical value for 95% confidence level, both sided test be:-

margin of error :-

95% confidence interval estimate of µ be:-

= (1038.24 , 1061.76 )

c).

sample size (n) = 90

sample mean () = 1050

z critical value for 99% confidence level, both sided test be:-

margin of error :-

99% confidence interval estimate of µ be:-

= (968.54 , 1131.46 )

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