Question 1105771: For each of the following problems, please provide the requested information.
. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
. (b) Identify the sampling distribution you will us: the standard normal or Student’s t. Explain the rationale for your choice. What is the value of the sample test statistic?
. (c) Find (or estimate) the P − value. Sketch the sampling distribution and show the area corre- sponding to the P − value.
(d) Find the critical value(s).
(e) Based on your answers for parts (a) to (d), will you reject or fail to reject the null hypothesis? Interpret your decision in the context of the application.
Assume that x is normally distributed. James gets stuck in traffic on his way to work, everyday for many years! On average he was always stuck for μ = 20 minutes. After a construction expanded the highway from 3 to 4 lanes. The traffic started moving more smoothly. A random selection of five days showed the delay to have a mean x ̄ = 15.2 minutes with a sample standard deviation of s = 6.3 minutes. Does this indicate that the population mean delay time due to traffic after the highway-expansion is shorter that what it used to be? Use significance level of 0.05.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This should be a one-tailed t-test, because a sample is taken and the sd of the sample is used to estimate the variance. One-tail may be done, because the expectation will be the delay should be shorter.
Ho: delay is same or worse
Ha: delay is less
alpha=0.05, critical value is t 0.95 df=4=-2.132
t=(15.2-20)/6.3/sqrt(5)
t=-4.8*sqrt(5)/6.3=-1.70
p-value=0.08
There is insignificant evidence to say that the mean time delay is less.
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