Question

Hi, can you help me answer this question please, thank you

Answer 1

In this case the population standard deviation is unknown. We only have the sample standard deviation s. Then,

the confidence interval formula for estimating the population mean is

`\bar{x}-T_c\frac{s}{\sqrt[]{n}}<\mu<\bar{x}+Tc\frac{s}{\sqrt[]{n}}`

where Tc is the critical T-value, which depends on the confidence level. For the 95% confidence level and n=26, the T value is

`T_C=2.060`

Then, by substituting this value and the given ones into the confidence interval, we have

`37-(2.060)\frac{11}{\sqrt[]{26}}<\mu<37+(2.060)\frac{11}{\sqrt[]{26}}`

which gives

`37-4.44399<\mu<37+4.44399`

By rounding to 3 decimal places, the answer is

`32.556<\mu<41.444`