Question

Listed below are brain volumes (cubic cm) of unrelated subjects used in a study. Use a 10% significance level to test the claim that the population of brain volumes has a mean equal to 1100.0 cu.cm.

Students will need to utilize the excel functions: t.dist(), t.dist.2t(), and t.dist.rt() in this activity.

1163

1057

1272

1079

1070

1173

1107

1347

1100

1204

Fill in the blanks with the appropriate responses:

Statistics
What is the sample mean: _____________cu. cm (use two decimal places in your answer)
What is the sample standard deviation: ____________cu. cm (use four decimal places in your answer)

Hypotheses
H₀: The mean brain volume is equal to 1100.0 cu.cm
H₁: The mean brain volume is __________to 1100.0 cu.cm
(type in “less than”, “greater than”, or “not equal to”)

Results
t = __________ (enter the test statistic, use 2 decimal places)
p-value = ____________(round answer to nearest thousandth of a percent – i.e. 0.012%)

Conclusion
We ___________sufficient evidence to support the claim that the mean brain volume is _____________-1100.0 cu.cm (p _____________0.10).
(Use “have” or “lack” for the first blank, “less than”, “greater than” or “not equal to” for the second blank and “<” or “>” for the final blank)

Answer 1

Part A:

Mean

Formula:

Mean = (1163+1057+...+1204)/10

So, Mean = 1157.2 cu cm.

Sample Standard Deviation

Formula:

By using this formula, the Sample Standard Deviation comes out to be: 95.001

Part B:

H₀: The mean brain volume is equal to 1100.0 cu.cm
H₁: The mean brain volume is not equal to 1100.0 cu.cm

This is because, it is a 2 tailed test.

Part C:

U₀ = 1100

X bar = 1157.2

s = 95

n = 10

So,

t = 1.904

Degree of Freedom = n-1 = 10-1 = 9 (n is the sample size)

P value for t = 1.904 is 0.0714

as it is a Two Tailed Test, so the P value will be halved...

So, P value = 0.035

Part D:

We have sufficient evidence to support the claim that the mean brain volume is not equal to 1100.0 cu.cm (p is less than (<) 0.10).

T Table:

End of the Solution...