Question

For each of the following​ situations, find the critical​ value(s) for z or t. ​a) H0​: pequals0.1 vs. HA​: pnot equals0.1 at alphaequals0.01 ​b) H0​: pequals0.5 vs. HA​: pgreater than0.5 at alphaequals0.05 ​c) H0​: muequals40 vs. HA​: munot equals40 at alphaequals0.05​; nequals22 ​d) H0​: pequals0.1 vs. HA​: pgreater than0.1 at alphaequals0.01​; nequals330 ​e) H0​: muequals50 vs. HA​: muless than50 at alphaequals0.05​; nequals1000

Answer 1

(a) For the given hypothesis, at significance level the critical value is given by-

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(b) For the given hypothesis, at significance level the critical value is given by-

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(c) For the given hypothesis, at significance level and with given sample size, the critical value is given by-

We have used a t-distribution because we have small sample, i.e.,

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(d) For the given hypothesis, at significance level , the critical value is given by-

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(e) For the given hypothesis, at significance level and with given sample size, the critical value is given by-

We have use Z because of large sample size, i.e.,