Mathematics, 17.03.2020 04:56 valeriestamann

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion, ^ p , to be within 0.04 of the true proportion, p (i. e., between 0.16 and 0.24)

Answers: 2

Show answers

Answers

Answer from: XxMikeLearnsxX9288

Roughly a 95% chance.

Step-by-step explanation:

The standard deviation of sample of size 'n' and with a proportion 'p' is given by:

$SD = \sqrt{\frac{p*(1-p)}{n} }$

In this case, in a sample of 400 residents with proportion 20%, the standard deviation is:

$SD=\sqrt{\frac{0.2*(1-0.2)}{400} }\\ SD=0.02$

The upper and lower limits proposed (0.16 and 0.24) are exactly two standard deviations above and below the mean of 0.20. According to the 95% rule, this interval comprehends 95% of all data. Therefore, there is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.

Answer from: maxout67

P(0.16 < $\hat p$ < 0.24) = 0.9546 or 95.5%

Step-by-step explanation:

We are given that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase.

Let p = % of the residents in a certain state that support an increase in the property tax = 20%

$\hat p$ = % of the residents in a certain state that support an increase in the

property tax in a sample of 400 residents

The one-sample z sore probability distribution for sample proportion is given by;

Z = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ~ N(0,1) where, n = sample residents = 400

So, probability that sample proportion will lie between 0.16 and 0.24 is given by = P(0.16 < $\hat p$ < 0.24)

P(0.16 < $\hat p$ < 0.24) = P( $\hat p$ < 0.24) - P( $\hat p \leq$ 0.16)

P( $\hat p$ < 0.24) = P( $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ < $\frac{0.24 -0.20}{\sqrt{\frac{0.24(1- 0.24)}{400} } }$ ) = P(Z < 1.87) = 0.96926

P( $\hat p$ $\leq$ 0.16) = P( $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ $\leq$ $\frac{0.16 -0.20}{\sqrt{\frac{0.16(1- 0.16)}{400} } }$ ) = P(Z < -2.18) = 1 - P(Z $\leq$ 2.18)

= 1 - 0.98537 = 0.01463

Therefore, P(0.16 < $\hat p$ < 0.24) = 0.96926 - 0.01463 = 0.9546

Hence, it is 95.5% likely that the sample proportion will lie between 0.16 and 0.24.

Answer from: Quest

i wish i could u

step-by-step explanation:

i wish i could u

Which is an x-intercept of the continuous function in the table

Answer from: Quest

what is the graph

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Amaple syrup producer records th amount of sap collected from each of his trees. the line plot shows the results for one day. what is the least amount of sap any one tree produced?

Answers: 1

Answer

Mathematics, 21.06.2019 18:10

True or false look at the picture pls : /

Answers: 2

Answer

Mathematics, 21.06.2019 19:10

Alogical argument that is presented in graphical form using boxes and arrows is called?

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Triangle knm is what is true about the sides of knm