Question

the global business travel association reported the domestic airfare for business travel for the current year and the previous year. below is a sample of flights with their domestic airfares shown for both years. do not round intermediate calculations.

Answer 1

Using a paired t test, the Pvalue is less than the value of the test statistic. Hence, we reject the Null hypothesis.

The hypothesis :

$H_{0} = μ_{d} ≤ 0$

$H_{1} = μ_{d} > 0$

The test statistic can be calculated thus :

Test statistic = $\frac{μ_{d}}{\frac{S_{d}}{\sqrt{n}}}$

• Sample size, n = 12

Using a calculator :

• Mean difference, $μ_{d} = 23$

• Standard deviation of difference, $S_{d} = 38.86$

Inputting the values into the formula :

Test statistic = $\frac{23}{\frac{38.86}{\sqrt{12}}}$

Test statistic = $\frac{23}{11.217} = 2.05$

Calculating the P-value :

• Degree of freedom, df = 12 - 1 = 1

• α = 0.05 (1 tail)

Pvalue = 0.03 (Pvalue calculator)

Since the Pvalue < α ; We reject the Null hypothesis.

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