A botanist measures the heights of 16 seedlings and obtains a mean and standard deviation of 72.5 cm and 4.5 cm,respectively.If seedling height is normally distributed,the 95% confidence interval for the mean height of seedlings in the population form which the sample was selected would be _____.
A)[62.91,82.09]
B)[70.30,74.70]
C)[70.10,74.90]
D)[70.54,74.46]
E)[71.90,73.10]

Question

Quizplus · Accepted Answer

We can use the formula:

Confidence interval = sample mean ± (critical value) x (standard error)

where the critical value can be found using a t-distribution table with degrees of freedom n-1 (n=sample size) and confidence level of 95%, which is 2.131 in this case.

The standard error can be calculated using the formula:

Standard error = sample standard deviation / sqrt(sample size)

Plugging in the values, we get:

Standard error = 4.5 / sqrt(16) = 1.125

Confidence interval = 72.5 ± 2.131 x 1.125 = [70.10, 74.90]

Therefore, the best choice is C, which matches this interval.

A Botanist Measures the Heights of 16 Seedlings and Obtains