Question

The historical on-time percentage for Amtrak's Sunset Limited is 10 percent. In July, the train was on time 1 times in 27 runs. Hint: Use Excel to calculate the cumulative binomial probability PX s 1 I n = 27, π = 0.10). Assume α = 0.1.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.10
Alternative hypothesis: P ≠ 0.10

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (σ) and compute the z-score test statistic (z).

σ = sqrt[ P * ( 1 - P ) / n ]

σ = 0.05774
z = (p - P) / σ

z = - 1.09

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.09 or greater than 1.09 Thus, the P-value = 0.2758

Interpret results. Since the P-value (0.2758) is greater than the significance level (0.10), we cannot reject the null hypothesis.