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2 years ago

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The essay lengths of 29 randomly sampled essays are used to estimate the mean of the population. What t-score should be used to

find the 95% confidence interval for the population mean? g

1 answer:

slavikrds [6]2 years ago

5 0

Answer:

A t-score of 1.701 should be used to find the 95% confidence interval for the population mean

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 29 - 1 = 28

Now, we have to find a value of T, which is found looking at the t table, with 28 degrees of freedom(y-axis) and a confidence level of 0.95( $t_{95}$ ). So we have T = 1.701.

A t-score of 1.701 should be used to find the 95% confidence interval for the population mean

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$\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[X]+E[X]^2]=E[X^2]-E[X]^2$

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$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx$

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