Question

Delta Flights: According to the Bureau of Transportation Statistics, 77.4% of Delta Airline’s flights arrived on time in 2010. The company is trying to improve on-time arrivals. They test the hypotheses H 0: p = 0.774 versus H a: p > 0.774. They calculate a P‐value of 0.03. Using a significance level of 0.05, which of the following is the best explanation for how to use the P‐value to reach a conclusion in this case? Group of answer choices Since the P‐value is less than the significance level, we reject the null hypothesis. Since the P‐value is less than the significance level, we fail to reject the null hypothesis. Since the P‐value is less than the significance level, we accept the null hypothesis.

Answer 1

The P-value is less than the significance level, so we reject the null hypothesis.

Step-by-step explanation:

The best explanation for how to use the P-value to reach a conclusion in this case is:

• Since the P-value is less than the significance level, we reject the null hypothesis.

In hypothesis testing, the P-value represents the probability of observing a test statistic as extreme as the one calculated or even more extreme, assuming that the null hypothesis is true. By comparing the P-value to the significance level (alpha), we can make a decision. In this case, since the P-value (0.03) is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence in support of the alternative hypothesis.

Answer 2

If the p-value is less than the significance level, we reject the null hypothesis.

Step-by-step explanation:

When we are trying to perform a right-sided hypothesis test (which is the case in this problem), we have a
`z_0` given by the significance level and a
`z_a` given by the alternative hypothesis.

`z_0` is a value such that the area under the normal curve N(0,1) is less than the level of significance, in this case 0.05, which is
`z_0=1.96`

`z_a` is a value that we find (if the sample size of the data we collet to reject the null hypothesis is big enough) after computing the following formula:

`z_a=(\bar x -\mu)/(s/√(n))`

where

`\bar x` is the mean of the sample

`\mu` is the mean established in the null hypothesis

`s` is the standard deviation of the sample

`n` is the size of the sample

If
`z_a` falls to the right of
`z_0` then we reject
`H_0`

because the area under the normal curve to the left of
`z_a` is less than 0.05.

But the area under the normal curve to the left of
`z_a` is precisely the p-value (see picture attached).

So, if the p-value is less than the significance level, we reject the null hypothesis.