Final answer:
To calculate the test statistic, we use the two-proportion z-test. The test statistic is approximately -0.784. We fail to reject the null hypothesis, indicating that there is insufficient evidence to conclude that the percentage of passengers using Wi-Fi has changed.
Step-by-step explanation:
To calculate the test statistic, we will use the two-proportion z-test. The null hypothesis (H0) states that the percentage of passengers who use Wi-Fi is 19%. The alternative hypothesis (Ha) is that the percentage has changed. From the survey, we have 100 passengers and 15% of them use Wi-Fi.
Let's calculate the test statistic:
p1 = 0.15 (sample proportion of Wi-Fi users)
p2 = 0.19 (hypothesized proportion)
n1 = 100 (sample size)
n2 = 100 (sample size)
We calculate the test statistic using the formula:
z = (p1 - p2) / sqrt((p * (1 - p)) / n1 + (p * (1 - p)) / n2)
where p = (n1 * p1 + n2 * p2) / (n1 + n2)
Substituting the values, we get:
p = (100 * 0.15 + 100 * 0.19) / (100 + 100) = 0.17
z = (0.15 - 0.19) / sqrt((0.17 * (1 - 0.17)) / 100 + (0.17 * (1 - 0.17)) / 100)
z = -0.04 / sqrt(0.000659 + 0.000659)
z ≈ -0.04 / 0.051
z ≈ -0.784
The test statistic is approximately -0.784. To make a decision, we compare the test statistic to the critical value.
Since the p-value is not given, we can't directly compare the test statistic to it. However, we can compare the test statistic to the critical value to see if it falls in the rejection region.
At a significance level of 0.05 (assuming it was not specified), the critical value for a two-tailed test is approximately ±1.96. Since -0.784 falls within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the percentage of passengers who use Wi-Fi has changed.