Obtain a 95% confidence interval for the mean weight

[TONYYEUNG]

Dear All,

Please help me to do the following questions, it is a new subject and it is so difficult to me:

A salmon fishing company is monitoring the weight of salmon in its ponds prior to harvest. A pilot sample of ten fish, randomly selected, shows a mean weight of 2.31 kilograms with a standard deviation of 0.17 kilogram.

(a) Obtain a 95% confidence interval for the mean weight of all salmon in the ponds.

(b) Using the standard deviation from the pilot survey as an estimate of the true variation of weights of salmon in the ponds, establish how many fish should be sampled to obtainan estimate of the mean weight of all the salmon in the ponds to within 0.03 kilogram with 95% confidence. (Take 2 as an approximation to the value of t.)

 

[galactus]

Using n=10, \(\displaystyle \overline{x}=2.31\), \(\displaystyle {\sigma}=0.17\)

Look up 95% CI in the z-table, z=1.96

\(\displaystyle \L\\E=z\frac{\sigma}{\sqrt{n}}\)

\(\displaystyle \L\\E=1.96\frac{0.17}{\sqrt{10}}=0.105\)

\(\displaystyle \overline{x}-E=2.31-0.105=2.205\)

\(\displaystyle \overline{x}+E=2.31+0.105=2.415\)

\(\displaystyle 2.205<{\mu}<2.415\)

With 95% confidence, you can say that the mean weight of the fish is between 2.205 and 2.415 kgs.