Question

Examine the given​ statement, then express the null hypothesis Upper H 0 and the alternative hypothesis Upper H 1 in symbolic form. High school teachers have incomes with a standard deviation that is less than ​$17 comma 500. Which of the following is the hypothesis test to be​ conducted? A. Upper H 0​: sigmagreater than​$17 comma 500 Upper H 1​: sigmaequals​$17 comma 500 B. Upper H 0​: sigmaequals​$17 comma 500 Upper H 1​: sigmagreater than​$17 comma 500 C. Upper H 0​: sigmaless than​$17 comma 500 Upper H 1​: sigmaequals​$17 comma 500 D. Upper H 0​: sigmaequals​$17 comma 500 Upper H 1​: sigmanot equals​$17 comma 500 E. Upper H 0​: sigmaequals​$17 comma 500 Upper H 1​: sigmaless than​$17 comma 500 F. Upper H 0​: sigmanot equals​$17 comma 500 Upper H 1​: sigmaequals​$17 comma 500

Answer 1

Solution:

We have to examine the given​ statement, then express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.
Statement: High school teachers have incomes with a standard deviation that is less than ​$17,500.

That is we have to test if standard deviation High school teachers have incomes is less than 17500

Since it is saying Less than, this is left tailed test.

Thus null and alternative hypothesis are:

Thus correct option is:

E. H₀​: sigma = $17,500 ; H₁​: sigma < ​$17,500