4,250,000 written in word form

A random sample of 500 adult residents of Maricopa County found that 356 were in favor of increasing the highway speed limit to

zzz [600]

Answer:

$z=1.04$

$p_v =2*P(Z>1.04)\approx 0.298$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ 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

$X_{PC}=297$ represent the number of residents of Pima County in favor of the increased speed limit

$X_{MC}=356$ represent the number of residents of Maricopa County in favor of the increased speed limit

$n_{PC}=400$ sample of Pima County selected

$n_{MC}=500$ sample of Maricopa County selected

$p_{PC}=\frac{297}{400}=0.743$ represent the proportion of residents of Pima County in favor of the increased speed limit

$p_{MC}=\frac{356}{500}=0.712$ represent the proportion of residents of Maricopa County in favor of the increased speed limit

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ 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: $p_{PC} - p_{MC}=0$

Alternative hypothesis: $p_{PC} - \mu_{MC} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{PC}-p_{MC}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{PC}}+\frac{1}{n_{MC}})}}$ (1)

Where $\hat p=\frac{X_{PC}+X_{MC}}{n_{PC}+n_{MC}}=\frac{297+356}{400+500}=0.726$

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:

$z=\frac{0.743-0.712}{\sqrt{0.726(1-0.726)(\frac{1}{400}+\frac{1}{500})}}=1.04$

4) Statistical decision

Since is a two side test the p value would be:

$p_v =2*P(Z>1.04)\approx 0.298$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ 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.

8 0

3 years ago

Which of the following is true for a median? Medians are affected by outliers. Medians can be calculated no matter how the data

Lady bird [3.3K]

Answer:

Option D) is true about median

Step-by-step explanation:

We are given the following information in the question:

Median:

The median is the middle number or the center of the data when the data is sorted in either ascending or descending order.

The median is not affected by the presence of any outliers since the data is sorted.

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$