Question

A random sample of n= 30 metal hardness depths has a standard deviation of 0.0885. After graphing the data, the experimenter notices that the histogram is approximately bell-shaped and symmetric. Test the null hypothesis that the population standard deviation is equal to 0.09 versus the two sided alternative. Use α =0.01.

Type out the complete hypothesis test (Be sure to label all steps) and write out the complete conclusion including your alpha level, test statistic value and p-value. Also make sure to include a critical value and what the rejection region would be.

Answer 1

σ: standard deviation of Sample

The Bonett method cannot be calculated for summarized data.

The chi-square method is valid only for the normal distribution.

Descriptive Statistics

N	StDev	Variance	95% CI for σ using Chi-Square
30	0.0885	0.00783	(0.0705, 0.1190)

Test

Null hypothesis	H₀: σ = 0.09
Alternative hypothesis	H₁: σ ≠ 0.09

Method	Test Statistic	DF	P-Value
Chi-Square	28.04	29	0.969

Since the p-value (0.969) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we can conclude that the population standard deviation is equal to 0.09.