Most air travelers now use e-tickets. Electronic ticketing...

Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less than paper ticketing. However, recently 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. $$\begin{array}{|llllllllll|}\hline 14 & 14 & 16 & 12 & 12 & 14 & 13 & 16 & 15 & 14 \\12 & 15 & 15 & 14 & 13 & 13 & 12 & 13 & 10 &13 \\\hline\end{array}$$ 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.

Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less than paper ticketing. However, recently 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.
$$\begin{array}{|llllllllll|}\hline 14 & 14 & 16 & 12 & 12 & 14 & 13 & 16 & 15 & 14 \\12 & 15 & 15 & 14 & 13 & 13 & 12 & 13 & 10 &13 \\\hline\end{array}$$
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.

Key Concepts

Random Sampling

Random sampling is the process of selecting a subset from a population in such a way that every member has an equal chance of being chosen. This concept is crucial because it helps ensure that the sample is representative of the overall population, thus allowing valid generalizations and reducing sampling bias.

Significance Level

The significance level, often set at 0.05, defines the threshold for rejecting the null hypothesis. It represents the probability of committing a Type I error, which is incorrectly rejecting the null hypothesis when it is true, and serves as a benchmark for evaluating the p-value obtained from the test.

Hypothesis Testing

This is a statistical method used to make inferences about a population parameter based on sample data. It involves formulating a null hypothesis (no effect or a specified value) and an alternative hypothesis (representing a deviation from the null), and then using sample statistics to determine whether to reject the null hypothesis at a predetermined significance level.

One-Sample t-Test

When the population standard deviation is unknown and the sample size is small, the one-sample t-test is appropriate for testing hypotheses about the mean. It uses the t-distribution to account for additional uncertainty in the estimation of the standard error, and it assesses whether the observed sample mean differs significantly from a hypothesized population mean.

Assumption of Normality

The validity of the one-sample t-test hinges on the assumption that the underlying population distribution is normal, especially when the sample size is small. This assumption justifies the use of the t-distribution, and it is often verified using visual techniques such as dot plots or histograms to examine the data’s distribution.

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