Question

1. We are managing a large soy bean farm. To estimate our revenues for the coming year, we need to estimate our crop yield. Soy bean yields are measured by pods/plant. We are planning for a yield of 40 pods/plant. We take a random sample of 64 soy bean plants and get a sample yield of 42.8 pods/plant with a sample standard deviation of 12.0 pods/plant.

1. Use Minitab to find the correct t multiplier, then compute by hand a 95% confidence interval for our population yield based on this sample. Confirm your answer using Minitab’s 1-sample t function. (Note that yield in pods/plant gives a mean, thus a t interval is used.)   
2. Interpret the interval. Are we 95% confident based on this interval, that we will have a yield of at least 40 pods/plant? No

Answer 1

we have given the sample size n = 64

sample mean = 42.8

sample standard deviation s = 12

since the population standard deviation is not known so we will use t test to find the confidence interval

the t multiplier using t table with 63 degree of freedom is 1.998

95% confidence interval is

=

=

= (39.80, 45.80)

using Minitab >stat>basic stat>one sample t we have

One-Sample T

N Mean StDev SE Mean 95% CI
64 42.80 12.00 1.50 (39.80, 45.80)

b ) since the value 40 lies in this interval so yes, we are 95% confident based on this interval, that we will have a yield of at least 40 pods/plant