Question

A sample of 21 observations was taken. The sample average (18.44) and the sample variance (2.90) were calculated. Take the hypothesis test by the three methods:

Ho µ = 19.5

Ha µ> 19.5

to. Calculating the appropriate limit in terms of Xb for a reliability of 97.5% (sample average). (10 pts)

 

b. Calculate the limit in terms of the appropriate test statistic for 97.5% reliability and find the corresponding test statistic. (10 pts)

 

c. Calculate the p-value for this hypothesis test. (10 pts)

Answer 1

Answer:

Given that,

The sample of 2 observations was taken.

i.e, n=21

The sample average(Xb) =18.44

The sample variance (V)=2.90

Then,

Standard deviation ()==1.703

The hypotheses test are,

(a).

The appropriate limit in terms of Xb for the reliability of 97.5%:

Let,

=1-97.5%=1-0.975=0.025

/2=0.0125

Then, z critical value is,

=2.24 (Two-tailed)

Then,

Confidence intervals:

Therefore, the appropriate limit in terms of Xb for the reliability of 97.5% is (17.607, 19.273).

(b).

Calculate the limits in terms of the appropriate test statistic for 97.5% reliability and find the corresponding test statistic:

The test statistic is Z-statistic:

where, Z ~ N(0,1) distribution.

Z=-2.849

The calculated value of the test statistic is less than the critical value.

We Reject H0.

(c).

Calculate the p-value for this hypothesis test:

The p-value at z=-2.9(Approx) and n=21 at =0.03 (Approx) is 0.0017 (Approximately). (Since from z-table)

Decision Rule:

If the p-value is less than alpha, Reject H0.

Here, the p-value is nearly zero,

We Reject H0.