Question

A) You wish to test the following claim (Ha) at a significance level of a = 0.02

Ho: u = 55.7

Ha : u =/ 55.7

You believe the population is normally distributed, but you know the standard deviation. You obtain the following sample of data:

90.6

71.6

75.1

106.7

What is the test statistic for this sample? ( report answer accurate to the 3 decimal places)

test statistic = --------

What is the p-value for this sample? ( answer 4 decimal places)

The p-value = -------

The p-value is ......

less than (or equal to ) a

greater than a

This test statistic leads to a decision to ....

1. reject the null

2. accept the null

3. fail to reject the null

Conclusion is that

1. There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.7

2. There is not sufficient evidence to warrant rejection of the that the population mean is not equal to 55.7

3. The sample data support the claim that the population mean is not equal to 55.7.

4. There is not sufficient sample evidence to support the claim that the population mean is not equal to 55.7.

Answer 1

SOLUTION:

From given data,

You wish to test the following claim (Ha) at a significance level of = 0.02

H_o: = 55.7

H_a : 55.7

You believe the population is normally distributed, but you know the standard deviation. You obtain the following sample of data:

=  90.6+71.6+75.1+106.7 = 344

Mean = = /n =344/4 = 86

Standard deviation = S = sqrt ((-)² /(n-1))

S = sqrt (((90.6-86)² +(71.6-86)² +(75.1-86)² +(106.7-86)² )/(4-1))

S = sqrt (775.82/3 )

S = 16.08125

What is the test statistic for this sample?

Test statistics:

t = ( - ) / (S /sqrt(n))

t = (86 - 55.7) / (16.08125 /sqrt(4))

t = 30.3 / 8.040625

test statistic = t = 3.768 ( report answer accurate to the 3 decimal places)

What is the p-value for this sample?

Degree of freedom = df = n-1 = 4-1 = 3

p-value at t = 3.768 with df = 3

p-value = 0.0327   ( answer 4 decimal places)

This test statistic leads to a decision:

Decision:

The p-value = 0.0327 is greater than significance level of = 0.02

Then we fail to reject the null

Answer : Option (3) is correct.

Conclusion is that

There is not sufficient evidence to warrant rejection of the that the population mean is not equal to 55.7

Answer : Option (2) is correct.