The proportion p of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 116 out of a random sample of 225 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%? OYes O No u Ix X ローロ X O S 2 Do OSO 0<0 S Р O

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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The proportion \( p \) of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 116 out of a random sample of 225 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.01 level of significance?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).

\[ H_0 : \]

\[ H_1 : \]

(b) Determine the type of test statistic to use.

\( \text{[Choose one]} \)

(c) Find the value of the test statistic. (Round to three or more decimal places.)

\[ \]

(d) Find the \( p \)-value. (Round to three or more decimal places.)

\[ \]

(e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%?

\( \text{[Yes]} \) \( \text{[No]} \) 

The right side of the image contains symbols and notations for mathematical expressions commonly used in hypothesis testing.
Transcribed Image Text:The proportion \( p \) of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 116 out of a random sample of 225 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \). \[ H_0 : \] \[ H_1 : \] (b) Determine the type of test statistic to use. \( \text{[Choose one]} \) (c) Find the value of the test statistic. (Round to three or more decimal places.) \[ \] (d) Find the \( p \)-value. (Round to three or more decimal places.) \[ \] (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%? \( \text{[Yes]} \) \( \text{[No]} \) The right side of the image contains symbols and notations for mathematical expressions commonly used in hypothesis testing.
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