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Menso is an organisation for people with high Intelligence Quotients (IQs). Menso is investigating the average IQ of primary school students to determine whether its entry requirements should be altered for younger people. A sample of 55 primary school students have been randomly selected from schools throughout the country. The sample mean IQ of those students was calculated as 92. It is known that the population standard deviation of the IQs of all people is 10. It is assumed that this standard deviation will also apply specifically to the IQs of the primary school students. Calculate the upper and lower bounds of the 95% confidence interval for the mean IQ of primary school students. Give your answers to 2 decimal places

Respuesta :

JeanaShupp

Answer: upper bound = 89.36 and lower bound = 94.64

Step-by-step explanation:

Confidence interval for mean : [tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\overline{x}[/tex] = sample mean , n= sample size , z* = two-tailed critical value, [tex]\sigma[/tex]= population standard deviation

As per given , we have

[tex]\overline{x}[/tex] = 92

n =  55

[tex]\sigma[/tex]= 10

Critical value for 95% confidence interval = 1.96

Required confidence interval :  [tex]92\pm (1.96)\dfrac{10}{\sqrt{55}}[/tex]

[tex]92\pm (1.96)(1.3484)\approx92\pm2.64\\\\= (92-2.64,\ 92+2.64)\\\\=(89.36,\ 94.64)[/tex]

Hence, for 95% confidence interval for the mean IQ of primary school students:

upper bound = 89.36 and lower bound = 94.64

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