Question

Research Question: Is the average weight (in grams) of all Emerald Ash Borer Beetle less than 3. To help, my Uncle Superfly (who happens to be a biologist) took a random sample of n=10 beetles from my back yard and recorded their weights.

They are:

1.5, 2, 3.5, 2.5, 1.5, 1.5, 2.5, 2, 2.5, 3

Answer 1

The data provided is:

	Data
	1.5
	2
	3.5
	2.5
	1.5
	1.5
	2.5
	2
	2.5
	3
Count	10
Mean	2.25
SD	0.677

will assume a level of significance of 0.05.

The provided sample mean is and the sample standard deviation is s=0.677, and the sample size is n=10.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 3

Ha: μ < 3

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a left-tailed test is tc​=−1.833.

The rejection region for this left-tailed test is R=t:t<−1.833

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t=−3.503<tc​=−1.833, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0033, and since p=0.0033<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 3, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval is 1.766<μ<2.734.

Graphically

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!