The mean arrival rate of flights at O’Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather the mean arrival rate is 200 flights per hour. (a) Set up a right-tailed decision rule at á=.025 to decide whether there has been a significant increase in the mean number of arrivals per hour. (b) Carry out the test and make the decision. Is it close? Would the decision be different if you used á = .01? (c) What assumptions are you making, if any? Flights

210 215 200 189 200 213 202 181 197 199
193 209 215 192 179 196 225 199 196 210
199 188 174 176 202 195 195 208 222 221

I'm confused.

To determine whether there has been a significant increase in the mean number of arrivals per hour at O'Hare Airport, we can perform a hypothesis test. Let's go through the steps.

Step 1: State the hypotheses.
- Null hypothesis (H₀): The mean number of arrivals per hour is equal to or less than 195 flights.
- Alternative hypothesis (H₁): The mean number of arrivals per hour is greater than 195 flights.

Step 2: Set the significance level.
In this case, the significance level (α) is 0.025.

Step 3: Formulate the decision rule.
Since the alternative hypothesis is that there is an increase in the mean, we need to set up a right-tailed decision rule. We will reject the null hypothesis if the test statistic is greater than the critical value.

Step 4: Calculate the test statistic.
To perform the hypothesis test, we need to calculate the test statistic, which is the z-score.

x̄ - μ
z = ------------------
σ / sqrt(n)

Where:
- x̄ is the sample mean (200 flights per hour).
- μ is the population mean (195 flights per hour).
- σ is the population standard deviation (13 flights).
- n is the sample size (30 days).

Step 5: Make the decision.
We compare the calculated test statistic with the critical value from the z-table.

Using the z-table, at a significance level of 0.025 (right-tailed test), the critical value is approximately 1.96.

If the calculated test statistic is greater than 1.96, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Now let's perform the calculations.

(a) Set up a right-tailed decision rule at α = 0.025:
- Critical value = 1.96

(b) Carry out the test and make the decision:
- Calculate the test statistic:
(200 - 195)
z = ------------------------ = 1.442
13 / sqrt(30)

The calculated test statistic, 1.442, is less than the critical value of 1.96. Therefore, we fail to reject the null hypothesis.

(c) Assumptions made:
- The sample is randomly selected.
- The data follows a normal distribution.
- The standard deviation of the population is known (historical standard deviation of 13 flights).

If we used α = 0.01 instead of α = 0.025, the critical value would be approximately 2.33. Since the calculated test statistic (1.442) is still less than 2.33, the decision would remain the same. We would still fail to reject the null hypothesis.