Answer: (97.98, 112.020)
Step-by-step explanation: We are going to construct a 95% confidence level interval for mean weight of melon.
From the parameters given to us, we conclude that the critical value of the interval will be gotten using a t distribution table, this is because sample size is less than 30 ( that's 20) and we are given the sample standard deviation (s =15lb)
Our parameters are given as follows
Sample mean =x = 105lb
Sample standard deviation =s= 15lb
Sample size = n = 20
To construct the 95% confidence interval, it denotes that we have a 5% level of significance.
The confidence interval formulae is given below as
u = x + tα/2 × s/√n...... For the upper limit
u = x - tα/2 × s/√n....... For the lower limit.
tα/2 = t critical value of the test ( which can be gotten using a t distribution table).
tα/2 is gotten by checking the value of degree of freedom (which is sample size - 1) against the level of significance for a 2 tailed test (α/2 = 0.025%) on a t distribution table
For upper limit, we have that
u = 105 + 2.093×15/√20
u = 105 + 2.093× (3.3541)
u = 105 + 7.020
u = 112.020.
For lower limit, we have that
u = 105 - 2.093×15/√20
u = 105 - 2.093× (3.3541)
u = 105 - 7.020
u = 97.98
Confidence interval (97.98, 112.020)
