To determine the effect of 100% nitrate on the growth of pea plants, several specimens were planted and then watered with 100% n
itrate every day. At the end of two weeks, the plants were measured. Here are data on seven of them: 17.5 14.5 15.2 14.0 17.3 18.0 13.8 Assume that these data are a random sample from a normal distribution N(μ, σ2).(a) Find the value of a point estimate of μ.(b) Find the value of a point estimate of σ.(c) Give the endpoints for a 90% confidence interval for μ.
1 answer:
Answer:
Step-by-step explanation:
From the attached photo
mean = 15.76
Standard deviation = 1.66
c) We want to determine a 90% confidence interval for the mean growth of pea plants
For a confidence level of 90%, the corresponding z value is 1.645. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
It becomes
15.76 ± 1.645 × 1.66/√7
= 15.76 ± 1.645 × 0.63
= 15.76 ± 1.04
The lower end of the confidence interval is 15.76 - 1.04 =14.72
The upper end of the confidence interval is 15.76 + 1.04 =16.8
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