Determine if all of the conditions have been met for the following hypothesis tests. If so,...

Determine if all of the conditions have been met for the following hypothesis tests. If so, write the hypotheses and identify the claim. (Do not conduct a full hypothesis test.)
(2 points for checking conditions and 2 points for hypotheses)

a. The Pew Research Center conducted a survey of 500 adults and found that 429 of them know what Twitter is. Use a 0.01 significance level to test the claim that at least 80% of adults know what Twitter is.

b. Listedbelowarethebodytemperaturesat8amonagivendayfromsamplesof men and women. Use a 10% significance level to test the claim that the men have a lower body temperature than women.

oo
Men: n = 30, X 97.45=F s 0.66 F =

oo Women: n=25, X 97.86=F s 0.89 F

Solutions

Expert Solution

(a) It is the case of Z test for the single population proportion, as (i) the sample which is used to conduct the survey, is reasonably random and (i) the sample size n = 500, is definitely large, since

Null hypothesis H0: At least 80% of adults know what Twitter is.That is P 0.80

Alternative hypothesis H1: Less than 80% of adults know what Twitter is. That is P 0.80

Claim: At least 80% of adults know what Twitter is. That is, the null hypothesis.

(b) It is the case of t-test, as (i) The samples which are used to test are reasonably random, (ii) the parent population(s) is(are) normal (iii) the sample sizes n1 and n2 are not sufficiently large i.e, both n1 and n2 30 and (iii) the population standard deviations are not given.

Null hypothesis H0: There is no significant difference between the body temperatures of men and women i.e,

Alternative hypothesis H1: The men have a lower body temperature than women i.e,

Claim: The men have a lower body temperature than women i. e, the alternative hypoyhesis.

orchestra answered 1 year ago

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