Consider the hypothesis test H0sigma sigma against H1sigma

Consider the hypothesis test H0:sigma = sigma against H1:sigma > sigma Suppose that the sample sizes are n1 = 20 and n2 = 8, and that s = 4.5 and s = 2.3. Use alpha = 0.01. Test the hypothesis Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but we suspect that the variability in concentration may differ between the two companies. The standard deviation of concentration in a random sample of n1 = 10 batches produced by company 1 is s1 =4.7 grams per liter, while for company 2, a random sample of n2 = 16 batches yields s2 = 5.8 grams per liter. Is there sufficient evidence to conclude that the two population variances differ? Use alpha = 0.05. A random sample of 500 adult residents of Maricopa County found that 385 were in favor of increasing the highway speed limit to 75 mph, while another sample of 400 adult residents of Pima County found that 267 were in favor of the increased speed limit. Do these data indicate that there is a difference in the support for increasing the speed limit between the residents of the two counties? Use alpha = 0.05. What is the P-valuc for this test?

Solution

chi square = 28-2/4.5/2.3 = 13.29

p value = 0.981

Difference is not significant.

s2/s1 = 5.8/4.1

chi square = 10+16-2/2 = 12

df =24

p value = 0.979

Accept null hypothesis.

Z-Score is 3.4199. The p-value is 0.00062. The result is significant at p <0.05. The proportion of Yes or No responses for Observation 1 is 0.77. The proportion for Observation 2 is 0.668

Hence there is significant difference