Question

Using seed 1411, generate a sample of size 50 from a uniformly distributed population over on the interval [10, 30].

a) Find a 90% confidence interval for the mean of the population.

x̄ ± t * s / √ n    (df = n-1)

b) Test the hypothesis H0: ?=18 versus ?1: ?<18μ=18 versus H1: μ<18; find the test statistic t, the P-value, and state your conclusion at the significance level α=0.1

(df = n - 1)

t = x̄ - μ / (s / √ n )

NEED STEP BY STEP ON HOW TO SOLVE USING EXCEL

Answer 1

Go to Data, then click on Data Analysis, select Random Number Generation from the options; In the new dialogue box, select the distribution is Uniform, give the variable as 1, number of random numbers as 50, parameters between 10 and 30 and set the random seed as 1411, give the output range as $A$1 and click on OK.

Now we calculate the following :

with the formula =AVERAGE(A1:A50) and store it in cell C1

s with the formula =STDEV.S(A1:A50) and store it in cell C2.

The critical value of t with df=49 and =0.1 is 1.68 and it is stored in cell C3.

Now the upper confidence limit is calculated using the following formula:

=C1+(C3*C2)/SQRT(50)

and the value is obtained as

19.8949

Now the lower confidence limit is calculated using the following formula:

=C1-(C3*C2)/SQRT(50)

and the value is obtained as

17.42419

(b)

Here we are to test  

Now the test statistic t is obtained by the following formula:

=(C1-18)/(C2/SQRT(50))

0.896933

The p-value is thus 0.187079

As the p-value is greater than 0.1, we fail to reject the null hypothesis at 10% level of significance and conclude that the mean of the random sample is 18.

Hopefully this will help you. If you are satisfied with the answer, give it a like. In case of any query, do comment. Thanks.