A sample of 14 commuters in Baltimore showed the average of the commuting times

Question

A sample of 14 commuters in Baltimore showed the average of the commuting times was 33.2 minutes. If the standard deviation was 8.3 minutes, find the 95% confidence interval of the true mean. Suppose that the average temperature in July in Tokyo is a random variable with parameters mu = 90 (measured in degrees), and =5. Find the probability that in a given year the average Temperature in July in Baltimore will be (a) above 100 degree F (b) below 95 degree F (c) between 85degree F and 95 degree F (d) below 88 degree F Find the critical chi-square value for 15 degrees of freedom when a = 0.10 and the test is left-tailed. Find the p-value when^2 = 10.869, and n = 21.

Explanation / Answer

10)for std error =std deviation/(n)1/2 =2.218

for 95% CI, z=1.96

hence confidence interval =sample mean -/+ z*std error =28.8523 ; 37.5477

11)a)P(X>100)=1-P(X<100)=1-P(Z<(100-90)/5)=1-P(Z<2)=1-0.97725=0.02275

b)P(X<95)=P(Z<1)=0.8413

c)P(85<X<95)=P(-1<z<1)=0.8413-0.1587=0.6827

d)P(X<88)=P(Z<-0.4)=0.3446

12) critical value =8.5468

13) p value=0.9495

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