Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cu

Question

Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, CA. This simple random sample was obtained at 3:30 p.m. on a weekday. Use a 0.05 significance level to test the claim of the highway engineer that the standard deviation of speeds is equal to 5.0 mi/h.    62 61 61 57 61 54 59 58 59 69 60 67 Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, CA. This simple random sample was obtained at 3:30 p.m. on a weekday. Use a 0.05 significance level to test the claim of the highway engineer that the standard deviation of speeds is equal to 5.0 mi/h.    62 61 61 57 61 54 59 58 59 69 60 67 Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, CA. This simple random sample was obtained at 3:30 p.m. on a weekday. Use a 0.05 significance level to test the claim of the highway engineer that the standard deviation of speeds is equal to 5.0 mi/h.    62 61 61 57 61 54 59 58 59 69 60 67

Explanation / Answer

we are given the alpha=0.05,n=12

62 61 61 57 61 54 59 58 59 69 60 67

we ahve to test the sanple variance with the hypothize variance

H0:

2=20

Ha:

2<20

   

for a lower one-tailed test

2>20

   

for

220

   

for a two-tailed test

Test Statistic:

T=(N1)(s/0)2

where N is the sample size and s is the sample standard deviation. The key element of this formula is the ratio s/0 which compares the ratio of the sample standard deviation to the target standard deviation. The more this ratio deviates from 1, the more likely we are to reject the null hypothesis.

calculate sample variance= 4.055

T=(N1)(s/0)2=(12-1)*(4.055/5)=8.92

T<2/2,N1 ,  for a two-tailed alternative  

chi critical value can be calculated in excel = chiiq.inv(0.05,11)=4.57

so we reject 8.92 >4.57, so we fail to reject the null hypothesis,

so there is sinsuficiant avidance that against claim.

thanks

H0:

2=20

Ha:

2<20

   

for a lower one-tailed test

2>20

   

for

220

   

for a two-tailed test

Test Statistic:

T=(N1)(s/0)2

where N is the sample size and s is the sample standard deviation. The key element of this formula is the ratio s/0 which compares the ratio of the sample standard deviation to the target standard deviation. The more this ratio deviates from 1, the more likely we are to reject the null hypothesis.

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