Question

Question 16: A previous study showed that 16.3 of teenage drivers get speeding tickets. You belive the percentage is lower than that. A random sample of 250 teenage drivers showed that 37 have had speeding tickets. Test this at the .05 significance level.

A: Verify the assumptions.

B: State the hypotheses.

C:What is the test statistics?

D:What is the p-value?

E:What is the conclusion?

Answer 1

given data and some necessary calculation :-

sample size (n) = 250

sample proportion () = 37/250 = 0.148

population proportion (p) = 16.3 % = 0.163

a).assumptions:-

i).the sample is a simple random sample .

ii).np = (250*0.163)= 40.75 >10 and n(1-p) = 250*(1-0.163) = 209.25 >10...

iii).the sample size can be assumed to be less than or equal to 10% of the population size

hence all the assumptions of 1 proportion Z test has been satisfied.

b).hypothesis:-

c).test statistic is:-

d).p value :-

[ as this is a left tailed test]

[ in any blank cell of excel type =NORMSDIST(- 0.6421) ]

e).decision:-

p value = 0.2604 >0.05 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support your believe that the percentage is lower than 16.3 % at 0.05 level of significance.

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