Answer: (97.98, 112.020)
Step-by-step explanation: We will create a 95% confidence interval for the average weight of melons.
Given the information, we determine that the critical value for the interval needs to be retrieved from a t distribution table due to the sample size being below 30 (specifically, 20), and we are provided with the sample standard deviation (s = 15 lb).
The parameters provided are:
Sample mean = x = 105 lb
Sample standard deviation = s = 15 lb
Sample size = n = 20
To establish the 95% confidence interval, we indicate that the level of significance is 5%.
The formula for the confidence interval is:
u = x + tα/2 × s/√n... for the upper limit
u = x - tα/2 × s/√n... for the lower limit.
tα/2 represents the critical value for the test (which will be determined using the t distribution table).
To derive tα/2, we look for the value based on the degrees of freedom (sample size - 1) against the significance level for a two-tailed test (α/2 = 0.025%) in a t distribution table.
For the upper limit, we calculate:
u = 105 + 2.093×15/√20
u = 105 + 2.093× (3.3541)
u = 105 + 7.020
u = 112.020.
<pfor the="" lower="" limit="" we="" find:="">
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)
</pfor>
