Question

The information about head sizes was collected over 18 pilots to determine the feasibility of using cheap cardboard callipers to make the measurements, instead of metal ones which were expensive and uncomfortable. The head size of each pilot was measured once using a cardboard calliper and again using a metal calliper. Is there any mean difference between the two sets of callipers? A researcher performed two analyses using Minitab with outputs on next page.

ANALYSIS I

Two-Sample T-Test and CI: Cardboard, Metal

Two-sample T for Cardboard vs Metal

            N    Mean StDev SE Mean

Cardboard 18 154.56   5.82      1.4

Metal      18 152.94   5.54      1.3

Difference = mu (Cardboard) - mu (Metal)

Estimate for difference: 1.61

95% CI for difference: (-2.24, 5.46)

T-Test of difference = 0 (vs not =): T-Value = 0.85 P-Value = 0.401 DF = 33

ANALYSIS II

Paired T-Test and CI: Cardboard, Metal

Paired T for Cardboard - Metal

             N    Mean StDev SE Mean

Cardboard   18 154.56   5.82     1.37

Metal       18 152.94   5.54     1.30

Difference 18   1.611 2.146    0.506

95% CI for mean difference: (0.544, 2.678)

T-Test of mean difference = 0 (vs not = 0): T-Value = 3.19 P-Value = 0.005

After having made a decision on the test at the significance of α = 0.05, the most appropriate conclusion in the context of research is

Question 25 options:

	There is not any significant difference between the population mean cardboard and metal measurements of head sizes.
	The population mean cardboard measurements is significantly greater than the population mean metal measurements.
	The population mean cardboard measurements is exactly the same as the population mean metal measurements.
	There is a significant difference between the population mean cardboard and metal measurements of head sizes.
	The population mean cardboard measurements is not significantly greater than the population meanmetal measurements.

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Answer 1

P-value is less than $\alpha$ =0.05

So, Reject the null hypothesis.

Answer

There is a significant difference between the population mean cardboard and metal measurements of head sizes.