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The cost of 6 flights is tabulated corresponding to the two types of booking: one day in advance and 30 days in advance.

It is claimed that the flights booked one day in advance are more expensive than flights booked 30 days in advance.

Null Hypothesis: The mean cost of flights booked one day in advance is more than the cost of flights booked 30 days in advance.

\({H_0}:{\mu _d} = 0\)

Alternative Hypothesis: The mean cost of flights booked one day in advance is more than the cost of flights booked 30 days in advance.

\({H_1}:{\mu _d} > 0\)

Here,\({\mu _d}\)is the population difference in the costs of the flights obtained by subtracting the cost of the flights booked 30 days in advance from the cost of the flights booked 1 day in advance.

The test is right-tailed.

The following table shows the differences in the systolic blood pressure levels for each matched pair:

The number of pairs is equal to\(n = 6\).

The mean value of the differences is computed below:

\(\begin{aligned} \bar d &= \frac{{\sum\limits_{i = 1}^n {{d_i}} }}{n}\\ &= \frac{{353 + 485 + ...... + 329}}{6}\\ &= 419.17\end{aligned}\)

The standard deviation of the differences is computed below:

\(\begin{aligned}{c}{s_d} &= \sqrt {\frac{{\sum\limits_{i = 1}^n {{{({d_i} - \bar d)}^2}} }}{{n - 1}}} \\ &= \sqrt {\frac{{{{\left( {353 - 419.17} \right)}^2} + {{\left( {485 - 419.17} \right)}^2} + ....... + {{\left( {329 - 419.17} \right)}^2}}}{{6 - 1}}} \\ &= 73.02\end{aligned}\)

The mean value of the differences for the population of matched pairs \(\left( {{\mu _d}} \right)\) is considered to be equal to 0.

The value of the test statistic is computed as shown:

\(\begin{aligned} t &= \frac{{\bar d - {\mu _d}}}{{\frac{{{s_d}}}{{\sqrt n }}}}\\ &= \frac{{419.17 - 0}}{{\frac{{73.02}}{{\sqrt 6 }}}}\\ &= 14.06\end{aligned}\)

The degrees of freedom are computed below:

\(\begin{aligned} df &= n - 1\\ &= 6 - 1\\ &= 5\end{aligned}\)

Refer to t-table:

The critical value of t at\(\alpha = 0.01\)and degrees of freedom equal to 5 for a right-tailed test is equal to 3.3649.

The p-value obtained using the test statistic value is equal to 0.00002.

Since the absolute value of the test statistic (14.06) is greater than the critical value and the p-value is less than 0.01, the null hypothesis is rejected.

There is enough evidence to conclude that flights booked one day in advance are costlier than flights booked 30 days in advance.

In order to save money, the passengers must plan their trips a month in advance and book their flights well in advance rather than going for flights just a day before the trip