PLEASE SHOW ANSWER FOR EACH STEP 96 97 98 99 According to statistics reported on

Question

PLEASE SHOW ANSWER FOR EACH STEP 96 97 98 99 According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Simple results, consistent with the 100 CNBC report, showed 42 of 204 vehicles were not covered by insurance. (See exercise 36 on page 369 of your textbook for a similar problem.) 101 102 103 104 105 106 107 108 109 110 Question 3 A Does the data show the proportion of vehicles not covered by insurance is different from 16% at =0.1? Step 1: HO: Ha: Step 2: 112 113 114 Fill in row 115 if the hypothesis is one tailed Reject HO if Fill in row 119 if the hypothesis is two tailed. The smaller number must be typed first. Reject HO if 116 118 119 120 121 122 123 or Step 4: Step 5: Step 6: HO 125 126 127 128 129 130 131 132 133 134 135 136 Question 3 B 137 138 139 140 Step 7: Fill in row 129 if the Z table is appropriate P-value Fill in row 133 if the t table is appropriate. The lower boundary must go on the left and the upper boundary on the right. P-value Construct a 99% confidence interval for the true proportion of vehicles not covered by insurance Lower Endpoint Upper Endpoint

Explanation / Answer

Step 1:

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.16
Ha:   p   =/=   0.16 [ANSWER]

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2.

As alpha = 0.1, two tailed,

zcrit = +/- 1.645 [ANSWER]

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3.

Hence,

reject Ho if z < -1.645 or z > 1.645 [ANSWER]

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4.

As we see, the hypothesized po =   0.16      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.205882353      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.025667558      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.787562069      

Hence,

zstat = 1.787562069 [ANSWER]

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5.

As z > 1.645, we REJECT HO. [ANSWER]

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6. There is significant evidence that the true proportion is different from 0.16.

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7.

As this is a    2   tailed test, then, getting the p value,  
          
p =    0.07384669   [ANSWER]  

or

0.05 < Pvalue < 0.10 [ANSWER]

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8.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.205882353          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.028309807          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.072921229          
lower bound = p^ - z(alpha/2) * sp =   0.132961124          
upper bound = p^ + z(alpha/2) * sp =    0.278803582          
              
Thus, the confidence interval is              
              
(   0.132961124   ,   0.278803582   ) [ANSWER]

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