Question

name:
hw 1.4

1. xena wanted to know the average height after 3 weeks of growth for a large bag of sunflower seeds. she planted a random sample of 8 sunflower seeds. after 3 weeks, the average height of the sunflower plants was 6.5 inches with an associated standard deviation of .625 inches. which of the following intervals give the plausible values for the true mean height of sunflower plants after 3 weeks of growth?

a) between 6.5 inches and 7.75 inches
b) between 5.25 inches and 6.5 inches
c) between 5.25 inches and 7.75 inches
d) between 1.25 inches and 3.5 inches

Explanation:

Step1: Recall confidence - interval concept

For a sample mean $\bar{x}$, the confidence - interval for the population mean $\mu$ is given by $\bar{x}\pm zs/\sqrt{n}$ (for large samples or known population standard deviation, here we assume a reasonable confidence level and since the sample size $n = 8$ is small, we can use a t - distribution in a more formal case, but for a rough estimate we can think of a few standard - deviation range). A common rule of thumb is to consider a range of about $\bar{x}\pm 2s$ for a reasonable level of confidence.

Step2: Calculate the range

We know that $\bar{x}=6.5$ inches and $s = 0.625$ inches.
The lower bound is $\bar{x}-2s=6.5 - 2\times0.625=6.5 - 1.25 = 5.25$ inches.
The upper bound is $\bar{x}+2s=6.5 + 2\times0.625=6.5+1.25 = 7.75$ inches.

Answer:

C. Between 5.25 inches and 7.75 inches