Is the water on your airline flight safe to drink? It is not feasible to analyze the water on every flight, so sampling is necessary. In August and September 2004 the EPA found bacterial contamination in water samples from the lavatories and gallery water taps on 20 of 158 randomly selected U.S. flights. Alarmed by the data, the EPA ordered sanitation improvements, and then tested water samples again in November and Decemeber 2004. In the second sample, bacterial contamination was found in 29 of 169 randomly sampled flights. (a) Use a left tailed test at a=.05 to check whether the percent of all flights with contaminated water was lower than the first sample. (b) find the p-value. (c) Discuss the question of significance versus imporance in this specfic application. (d). Test whether normality may be assumed. (Data are from The Wall Street Journal, November 10, 2004 and January 20, 2005.)
In order to answer the given statistical questions, we need to perform various steps. Let's break them down one by one:
(a) Hypothesis testing:
To test whether the percent of all flights with contaminated water was lower than the first sample, we need to set up the null and alternative hypothesis.
Null hypothesis (H0): The percent of all flights with contaminated water in the second sample is not lower than the first sample.
Alternative hypothesis (Ha): The percent of all flights with contaminated water in the second sample is lower than the first sample.
Since we are testing if the second sample is lower than the first sample, it is a left-tailed test.
(b) Finding the p-value:
To find the p-value, we need to calculate the test statistic and refer to the t-distribution table or use statistical software to obtain it. The test statistic formula depends on the sample sizes, sample means, and sample variances. However, the information provided in the question does not explicitly mention the sample means or variances. Therefore, it is not possible to calculate the p-value without that information.
(c) Significance versus importance:
In this specific application, the question of significance versus importance arises. Significance refers to the statistical significance of a result, while importance refers to the practical or real-world significance.
Even if the results show a statistically significant difference between the two samples, the practical importance depends on the context. Factors such as the severity of bacterial contamination, potential health risks, and the effectiveness of the sanitation improvements ordered by the EPA will affect the determination of importance.
(d) Testing normality assumption:
To test whether normality may be assumed, we can use various statistical tests such as the Shapiro-Wilk test or the Anderson-Darling test. However, the question does not provide the necessary sample data, so it is not possible to test for normality.
In summary, without the necessary sample data and statistical calculations, we cannot fully answer the questions (a), (b), (c), and (d) regarding the bacterial contamination in airline flight water.