Question

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. At \alpha = .05, we would reject the null hypothesis.
a. True
b. False

Answer 1

Answer:

b) False

Calculated value Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

Step-by-step explanation:

Explanation:-

Step:- (1)

Given data the opinion poll recently sampled 1500 voting age citizens.

Given sample size 'n' = 1500

Given data the opinion poll recently sampled 1500 voting age citizens in selected 1020 of the sampled citizens were in favor of an increase in cigarette taxes.

The sample proportion$'p' = \frac{1020}{1500} = 0.68$

Given data the state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66

Population proportion 'P' =0.66

                                      Q  = 1-P

                                      Q = 1-0.66 = 0.34

Null hypothesis :H₀: 'P' >0.66

Alternative hypothesis: H₀: 'P' <0.66

Level of significance ∝=0.05

Step:-(2)

The test statistic

                             $Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

                            $Z = \frac{0.68-0.66}{\sqrt{\frac{0.66 X 0.34}{1500} } }$

                            Z  =  1.635

The calculated value   Z  =  1.635

The tabulated value Z = 1.96 at ∝=0.05 level of significance.

Therefore  Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

The alternative hypothesis is rejected.

Conclusion:-

The null hypothesis is accepted at 0.05 level of significance.

The proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66