contestada

An SRS of 350 350 high school seniors gained an average of ¯ x = 22.61 x¯=22.61 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ = 53.63 . σ=53.63. We want to estimate the mean change in score μ μ in the population of all high school seniors. (a) Using the 68 68 – 95 95 – 99.7 99.7 Rule or the z - z- table (Table A), give a 95 % 95% confidence interval ( a , b ) (a,b) for μ μ based on this sample.

Respuesta :

JeanaShupp

Answer:  (16.9914, 28.2286).

Step-by-step explanation:

The formula to find the confidence interval for population mean is given by :-

[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = Sample mean

[tex]\sigma[/tex]= Population standard deviation

n= Sample size.

z* = Critical value.

Let μ be the mean change in score  in the population of all high school seniors.

As per given ,  we have

n= 350

[tex]\overline{x}=22.61[/tex]

[tex]\sigma=53.63[/tex]

The critical z-value for 95% confidence interval is z*= 1.96 [From z-table]

Substitute all the value in formula , we get

[tex]22.61\pm (1.96)\dfrac{53.63}{\sqrt{350}}[/tex]

[tex]=22.61\pm (1.96)\dfrac{53.63}{18.708287}[/tex]

[tex]=22.61\pm (1.96)(2.8666)[/tex]

[tex]=22.61\pm (5.6186)[/tex]

[tex]=(22.61-5.6186,\ 22.61+5.6186) =(16.9914,\ 28.2286)[/tex]

Hence, the 95% confidence interval for [tex]\mu[/tex] is (16.9914, 28.2286).

Otras preguntas