Question

Hi I had question about finding the critical values of an independent, ,random, two sample test( assuming equality of variances)

The question:

Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. A study published in the Journal of Nutrition compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan.Amongthe nutrients consideredwasprotein.Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 females vegetarians and 53 female omnivores yielded the following summary statistics, in grams, on daily protein intake. Vegetarians Omnivores ?? ̅̅̅̅ = ??. ?? ?? ̅̅̅̅ = ??. ?? s1 = 18.82 s2 = 18.97 n1 = 51 n2 = 53 Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level. Assume equality of variances.

Answer 1

n1=51, n2=53,

=39.04, = 49.92

s1 = 18.82, s2 = 18.97

= 1% = 0.01

Null and alternative hypothesis is

Ho:

Ha:

Calculate test statistics

t= −2.935

test statistics= −2.935

now calculate t critical values for two tailed test

wih = 0.01 and df= n1+n2-2 = 51 + 53-2 = 102

using t table we get

Critical values = 2.625

Critical values are = ( -2.625 , 2.625 )

since,

(test statistics= −2.935) < (Critical value = -2.625 )

test statistics lies in rejection region,

Hence,

the null hypothesis is rejected.

Conclusion:

Therefore, there is enough evidence to support the claim that the mean daily protein intakes of female vegetarians and female omnivores differ.