Need some help ASAP and work shown. Ps; If you answer I’ll mark you brainliest.
2 answers:
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Answer:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the proportion of people in favor of the increased speed limit not differs significantly between the two groups.
Step-by-step explanation:
1) Data given and notation
represent the number of residents of Pima County in favor of the increased speed limit
represent the number of residents of Maricopa County in favor of the increased speed limit
sample of Pima County selected
sample of Maricopa County selected
represent the proportion of residents of Pima County in favor of the increased speed limit
represent the proportion of residents of Maricopa County in favor of the increased speed limit
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference in the support for in increasing the speed limit between the residents of the two counties, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
Since is a two side test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the proportion of people in favor of the increased speed limit not differs significantly between the two groups.