Question

5. (a) A manufacturer of liquid soup produces a bottle with an advertised content of 310 mil. Sixteen botles are randomly selected and found to have the fotlowing contents, in ml. ,3?? 303 251 312 300 r 296 309 Tm Use the Wilcoxon signed-rank test at l0% level of significance to decide whether the mean content is less than advertised (7 mks) (b) A simple random sample of 35 new models of vehicles yieided the folowing data on fuel tank capacity, in gallons, 17.2 23.1 17.5 15.7 19.8 16.9 15.3 18.5 18.5 25.5 18.0 17.5 14.5 20.0 17.0 20.0 24.0 26.0 18.1 21.0 19.3 20.0 20.0 12.5 13.2 15.9 145 22.2 21.114.4 25.0 26.4 169 16.4 23.0 ret you i. Find a point estimate for the mean fuel tank capacity of all new automobile modals Inter answer in words (2 mks) Determine and interpreted a 95.44% confidence interval for the mean fuel tank capacity of all new automobile models. Assume ? 3.50 gallons (3 mks) ii. How would you decide whether fuel tank capacities for new automobile models are spproximately normalily distributed (2 mks)

Answer 1

Solutionbi:

point estimate=sample mean=xbar=664.9/35=18.997

Solutionbii:

Given sigma=3.5

95.44% confidence interval for population mean is

xbar-z*sigma/sqrt(n),xbar+z*sigma/sqrt(n)

18.99714-1.999*3.5/sqrt(35),18.99714+1.999*3.5/sqrt(35)

17.814,20.18

17.814< $\mu$ <20.18

lower limit=17.814

upper limit=20.18

we are 95.44% confident that the true popualtion mean lies in between

17.814 and 20.18

Solutionbiii:

sample size=n=35

given sample size is large sample

n>30

large sample follows normal distribution

According to centarl limit theorem follows normal distribution