Question

Different types of bees are very similar in appearance. Statistical analysis of certain measurements, like wing width, can be used to distinguish one kind of bee from another.

The wing width for a specific type of honeybee is approximately normally distributed with a mean of 2.82 millimeters (mm). A random sample of 10 bees is taken from a hive and the wing widths are given below.

Wing Width Measurements (mm)

2.88	2.83	2.91	2.83	2.94
2.87	2.80	2.80	2.83	2.88

Based on hypothesis test, what can be concluded concerning the bees from the hive?

Assume the level of significance is 0.05.

Select One:

A) There is not enough information to form a valid conclusion for this hypothesis test.

B) At the 0.05 significance level, we can conclude that the bees in the hive are the same species of bees that have mean wing width of 2.82 mm.

C) At the 0.05 significance level, there is sufficient evidence to conclude that the bees from the hive are not the same species of bees that have mean wing width of 2.82 mm.

D) At the 0.05 significance level, there is not sufficient evidence to conclude that the bees in the hive are a different than the species of bees that have mean wing width of 2.82 mm.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.82
Alternative Hypothesis, Ha: μ ≠ 2.82

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.857 - 2.82)/(0.0467/sqrt(10))
t = 2.5054

P-value Approach
P-value = 0.0336
As P-value < 0.05, reject the null hypothesis.

B) At the 0.05 significance level, we can conclude that the bees in the hive are the same species of bees that have mean wing width of 2.82 mm.