Question

Wind Mountain is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites the number of such sherds was counted in local dwelling excavations.

Site I Site II Site III
51 47 33
45 19 57
32 9 62
19 18 28
25 28
57 22
35
Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Test given b807b7c2-a348-4cb7-8322-f58461059cce.GIF.
What is the level of significance?
a. 90%
b. 1%
c. 5%
d. 99%
e. 95%

Answer 1

Without the ANOVA results, we cannot determine whether to reject the null hypothesis, but the traditionally used level of significance for hypothesis tests is 5%, corresponding to a 95% confidence level.

Step-by-step explanation:

The students asking whether to reject or not the claim that there's no difference in the population mean of Mimbres classic black-on-white sherd counts at three archaeological sites requires a statistical hypothesis test, specifically an ANOVA (Analysis of Variance) due to multiple groups being compared. To determine whether to reject the null hypothesis, we would look at the p-value obtained from the ANOVA test and compare it to the level of significance. The level of significance is given in the multiple-choice options, which are different confidence levels.

If the p-value is less than the chosen significance level, we would reject the null hypothesis, indicating that there is a statistically significant difference in the mean number of sherds at the different sites. As the actual p-value and ANOVA results are not provided in the question, we can't perform the exact test. However, the student asks for the level of significance, which corresponds to the confidence levels provided in the choices.

The traditionally used level of significance for many hypothesis tests is 5% (choice c), which corresponds to a 95% confidence level. This is the level at which most researchers are willing to conclude that a statistically significant difference exists.

Answer 2

Step-by-step explanation:

Hello!

This is an example of an ANOVA hypothesis test, where you'll compare the population means of the number of broken Mimbres in three different excavation sites.

The variable of interest is

Y: Number of broken pieces of prehistoric Native American clay vessels, called Mimbres in an excavation site.

Factor: Site

Treatments: 1, 2, 3

You are asked to identify the level of significance of the test. This value is the probability of committing Type I error, that is, when you fail to reject a false null hypothesis and is always represented with the Greek letter alpha "α"

This level is determined by the researcher when he is designing the experiment and statistical analysis. Normally you'd want this level to be as small as possible to be sure you didn't commit any mistake when deciding over the hypotheses.

The mos common values are 0.01, 0.05 or 0.1 and it can also be expressed as percentages 1%, 5% or 10%. Having a probability of making a mistake greater than 10% is too high so normally you would not encounter significance levels greater than 10%

With this in mind options b. 1% and c. 5% are valid values for α.

Have a nice day!

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