Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 21, 14, 13, 24, 17, 22, 25, 12

Required:
a. Calculate the sample mean and the sample standard deviation.
b. Construct the 90% confidence interval for the population mean.
c. Construct the 95% confidence interval for the population mean

a

     ,  

b

c

Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

Generally the standard deviation is mathematically evaluated as

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

Next we obtain the critical value of    from the normal distribution table the value is  

The margin of error is mathematically represented as

=>    

=>    

The 90% confidence interval is evaluated as

substituting values

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

Next we obtain the critical value of    from the normal distribution table the value is  

The margin of error is mathematically represented as

=>    

=>    

The 95% confidence interval is evaluated as

substituting values

step-by-step explanation:

x-intercept:

(

−

1

+

√

7

,

0

)

,

(

−

1

−

√

7

,

0

)

y-intercept:

(

0

,

−

6

)