3. Hypothesis tests about a population mean, population standard deviation unkno
ID: 2949392 • Letter: 3
Question
3. Hypothesis tests about a population mean, population standard deviation unknown Aa Aa E Airlines compute the weight of outbound flights using either standard average weights provided by the Federal Aviation Administration (FAA) or weights obtained from their own sample surveys. The FAA standard average weight for a passenger's carry-on items (personal items plus carry-on bags) is 16 pounds Many airline companies have begun implementing fees for checked bags. Economic theory predicts that passengers will respond to the increase in the price of a checked bag by substituting carry-on bags for checked bags. As a result, the mean weight of a passenger's carry-on items is expected to increase after the implementation of the checked-bag fee. Suppose that a particular airline's passengers had a mean weight for their carry-on items of 16 pounds, the FAA standard average weight, before implementation of the checked-bag fee. The airline conducts a hypothesis test to determine whether the current mean weight of its passengers' carry-on items is more than 16 pounds. It selects a random sample of 67 passengers and weighs their carry-on items. The sample mean is R17.1 pounds, and the sample standard deviation is s = 6.0 pounds. The airline uses a significance level of ? = .05 to conduct its hypothesis test. The hypothesis test is test. The test statistic follows a distribution. The value of the test statistic isExplanation / Answer
Solution:-
The hypothesis one sample test.
The test hypothesis test follows a t-distribution.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 16
Alternative hypothesis: u > 16
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.73302
DF = n - 1
D.F = 66
t = (x - u) / SE
t = 1.50
tcritical = 1.668
Reject H0 if t > 1.668
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
Interpret results. Since the t-value (1.50) is less than the critical value, hence we cannot reject the null hypothesis.
The p-value is 0.069.
Using critical value approach, the null hypothesis is not rejected, becuase t-value (1.50) is less than the critical value. Using the p-value approach, the null hypothesis is not rejected, because p-value(0.069) is greater than 0.05. Therefore, you can conclude that the mean weight of the airline's passenger's carry-on items has increased after the implementation of the checked-bag fee.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.