Complete the following problem Make sure you show the follow

Complete the following problem. Make sure you show the following for each hypothesis test:

a)     H₀

b)     H₁

c)      the test statistic (round to the nearest thousandth)

d)     the critical value(s)

e)     the P-value (round to the nearest thousandth, use 0⁺ if necessary)

f)      the conclusion (reject H₀ or fail to reject H₀)

g)     the final conclusion stated in non-technical terms

Assume all requirements are met to complete each of the hypothesis tests. If a significance level is not given, think about the seriousness of a type I error to determine which level of significance to use.

Question 1. 1. The Consolidated Package Delivery Service (CPDS) is considering moving to a new location. Previous records show the current daily mean travel distance of the delivery trucks from the old location is 214 mi. In trial runs of 12 delivery trucks from the new location, the mean and standard deviation for delivery distances are found to be 198 mi and 42 mi, respectively. Does the daily mean travel distance from the new location appear to be different from 214 mi? The company wants to be very sure about the decision about the mean travel distance from the new location.

Solution

Set up null and alternate as

H0: mu =214

Ha: mu not equals 214.

Two sided test

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As sample size n =12 is very small t test can be used.

Degrees of freedom: 11

t-statistic: -1.31965776

Critical t-value (two-tailed): +/- 2.20098

Two-tailed probability P(h = x): 0.2138

Two-tailed probability P(h ? x): 0.7862

p value for null hypothesis is 0.2138 >0.05

Hence 95% level, accept null hypothesis that sample mean is equal to population mean.