# Statistics Hypothesis

## Sample: Hypothesis Tests

**Question:**

At recent times, the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below:

14 12 14 15 16 15 12 14 12 13 14 13 13 12 16 13 15 10 14 13

At the .05 significance level can the watchdog agency conclude the mean number of complaints per airport is less than 15 per month?

**a.**What assumption is necessary before conducting a test of hypothesis?

**b.**Plot the number of complaints per airport in a frequency distribution or a dot plot. Is it reasonable to conclude that the population follows a normal distribution?

**c.**Conduct a test of hypothesis and interpret the results.

******Calculate it in minitab too.**

**Solution:**

**a. What assumption is necessary before conducting a test of hypothesis?**

The assumptions for the one-sample t-test are

Measurements are interval scale or better

Observations are independent of each other

The scores in the parent population are normally distributed.

**b. Plot the number of complaints per airport in a frequency distribution or a dot plot. Is it reasonable to conclude that the population follows a normal distribution?**

It is reasonable to conclude that the population follows a normal distribution.

**c. Conduct a test of hypothesis and interpret the results.**

Null Hypothesis:

Null Hypothesis:

H0: m = 15

**Alternative Hypothesis:**

H1: m < 15

Since the sample size is (n = 20 < 30) small, we can test the above hypothesis by the use of small sample test (t-test) as follows:

**Test Statistic:**

t =

We obtain the result using Minitab

**One-Sample T: C1 **

Test of mu = 15 vs < 15

95% Upper

Variable N Mean StDev SE Mean Bound T P

C1 20 13.500 1.504 0.336 14.082 -4.46 0.000

**Conclusion:**

At α=0.05, since the p value is < 0.05, we reject the null hypothesis, thus we conclude that the mean number of complaints per airport is less than 15 per month.

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