Name Is there enough evidence to conclude that the proportio

Name: Is there enough evidence to conclude that the proportion of the White vehicles differs from the national proportion of 28%? 2. Use the following sample data that has been collected by your instructor over the past few years. Of the 424 students, 107 had a white vehicle. Show all 5 steps and use 10% level of significance. Step 1: Formulate the Null and Alternative Hypothesis (4 pts) Step 2: Record the Level of significance and the sample proportion. (2 pts) Step 3: Record the Test Statistic with proper symbol (2 pts) Step 4: Record the P-value and interpret the P-value using the context of the problem (5 pts) Step 5: What is the final decision AND interpret the final decision by using the context of the problem. (5 pts)

Solution

1.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.28
Ha:   p   =/=   0.28 [ANSWER]

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2.

Here, level of significance = 0.10. [ANSWER]

As we see, the hypothesized po =   0.28      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.252358491 [ANSWER, SAMPLE PROPORTION]

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3.      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.021805314      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.267650171   [ANSWER TEST STATISTIC]

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4.  
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.204922907   [ANSWER, P VALUE]  

Thus, there is a probability of 0.2049 that we can get a value at least this extremely far from the population proportion.

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Thus, we fail to reject Ho, as P > 0.10.

There is no significant evidence that the sample data has a proportion different from the national proportion.