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2 years ago

7

Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the tr

ue proportion is 0.07. If 313 are sampled, what is the probability that the sample proportion will be less than 0.04

1 answer:

serg [7]2 years ago

5 0

The probability that the sample proportion will be less than 0.04 is <u>0.0188 or 1.88%</u>.

The true proportion given to us (p) = 0.07.

The sample size is given to us (n) = 313.

The standard deviation can be calculated as (s) = √[{p(1 - p)}/n] = √[{0.07(1 - 0.07)}/313] = √{0.07*0.93/313} = √0.000207987 = 0.0144217.

The mean (μ) = p = 0.07.

Since np = 12.52 and n(1 - p) = 291.09 are both greater than 5, the sample is normally distributed.

We are asked the probability that the sample proportion will be less than 0.04.

Using normal distribution, this can be shown as:

P(X < 0.04),

= P(Z < {(0.04-0.07)/0.0144217}) {Using the formula Z = (x - μ)/s},

= P(Z < -2.0802)

= 0.0188 or 1.88% {From table}.

Thus, the probability that the sample proportion will be less than 0.04 is <u>0.0188 or 1.88%</u>.

Learn more about the probability of sampling distributions at

brainly.com/question/15520013

#SPJ4

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tensa zangetsu [6.8K]

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Hope this helps!

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3 years ago

Read 2 more answers

Either use technology to find the P-value or use

Akimi4 [234]

Answer:

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation

$\bar X$ represent the mean

$s$ represent the sample standard deviation

$n=21$ sample size

$\mu_o =140$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t=-0.024 would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:

Null hypothesis: $\mu \geq 140$

Alternative hypothesis: $\mu < 140$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

The statistic is given by: $t = -0.024$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected $\alpah=0.01,0.05,0.1$

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The balloon’s vertical distance above the ground is 570.3 feet

<h3>Angle of elevation and depression</h3>

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2 years ago

Given that y is directly proportional to x. If y = 30 and x= 5, write an equation that connects y with x.

Licemer1 [7]

Given:

y is directly proportional to x.

$y=30$ when $x=5$

To find:

The equation that connects y with x.

Solution:

It is given that, y is directly proportional to x. So,

$y\propto x$

$y=kx$ ...(i)

Where, k is the constant of proportionality.

We have, $y=30$ when $x=5$ . Substituting these values in (i), we get

$30=k(5)$

Divide both sides by 5.

$\dfrac{30}{5}=k$

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Substituting $k=6$ in (i), we get

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