A Representative from Ford Motor Company wanted to know how the lifespan of Ford

Question

A Representative from Ford Motor Company wanted to know how the lifespan of Ford automobiles compared to the lifespan of other sutomobiles in the United States. This representative knew that the united states was .50, with population mean lifespan of 8 years. He selected a random sample of 25 ford cars and asked their former owners about the lifespan of the cars. The mean lifespan from this sample was 7.5 years. Using a non-directional test from the population in terms of lifespan. Be sure and state the null and alternative hypotheses. Also, construct the 95% confidence interval for the above.

Explanation / Answer

First, record what you know: u=8 sigma (pop std)= .5 n=25 xbar (sample mean)= 7.5 alpha (1- confidence interval)= 1-.95=.05 Second, set up the null (Ho) and alternative (Ha) hypotheses. NOTE:non-directional = two-tail Ho: u=8 Ha: u NOT = 8 Third, write and apply formula: z= (xbar-u)/(sigma/square root of n) = (7.5-8)/(.5/square root of25)= -.5/.1= -5/1 = -5 Fourth, note that at the 95% confidence level, the correspondingz-values for a two-tailed test are +/-1.96. The rule. Ourcalculated z-value is -.5 As -5 lies to the left of -1.96 it is inthe "rejection zone." Consequently,we REJECT the null hypothesis(Ho) and CONCLUDE that the means are SIGNIFICANTLY DIFFERENT AT THE95% CONFIDENCE LEVEL. Good luck!

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