Question

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

Answer 1

We have to find the margin of error at a 90% confidence level for estimating the population mean.

The sample size is n = 22, the sample mean is M = 35 and the sample standard deviation is s = 3.

In this case, we don't know the population standard deviation (σ). We have to estimate it from the sample standard deviation.

To do that, we use the Student's t distribution instead of the normal distribution.

When σ is not known, s divided by the square root of N is used as an estimate of σ:

`s_M=(s)/(√(N))=(3)/(√(22))=(3)/(4.69)=0.64`

The degrees of freedom for this sample size are:

`df=n-1=22-1=21`

The t-value for a 90% confidence interval and 21 degrees of freedom is t = 1.721.

The margin of error (MOE) can be calculated as:

`MOE=t\cdot s_M=1.721\cdot0.64\approx1.10`

Answer: the margin of error is 1.10.