The maturation time of maize plants follows the normal distribution. We follow 30 plants and it is seen that they reach maturity in 4 months. Construct a 95% confidence interval for the maturation time of the maize plant population.

Bayobusalue

Bayobusalue

Answered question

2022-11-13

In question I do not get any sigma, I know I can do the t student test based on degrees on freedom if I do not have the population st.dev, but in my case I do not even have the sample st.dev, can it be solved or the teacher made a mistake in the text ?
"The maturation time of maize plants follows the normal distribution. We follow 30 plants and it is seen that they reach maturity in 4 months. Construct a 95% confidence interval for the maturation time of the maize plant population."
In order to find the margin of error i still need S (the sample st.dev) no ?
Otherwise how can i proceed ? Chi squared ?

Answer & Explanation

Cindy Mercer

Cindy Mercer

Beginner2022-11-14Added 13 answers

Without any information about either the assumed or observed variance in the maturation time, it is not possible to construct a confidence interval or any interval estimate of the mean. You could leave it as an unknown quantity; e.g., if the sample variance is s 2 , then a 95% confidence interval can be constructed as
4 ± t 29 , 0.025 s 30
where t ν , α / 2 is the upper α / 2 quantile of a student t distribution with ν degrees of freedom. In this case,
t 29 , 0.025 2.04523 ,
thus the CI for the mean maturation time as measured in months, is
4 ± 0.373406 s ,
where s is the sample standard deviation.

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