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amid [387]
3 years ago
6

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe

n designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.05?
If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

a. If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.
b. If the confidence level is increased, then the sample size would need to decrease because increasing the sample size would create an even larger interval.
c. If the confidence level is increased, then the sample size would need to decrease because we would like the proportion of people who buckle up to be around 50%.
d. If the confidence level is increased, then the sample size would not be affected.
Mathematics
1 answer:
podryga [215]3 years ago
8 0

Answer:

The value  is  n = 384

The correct option is a

Step-by-step explanation:

From the question we are told that

   The margin of error is  E =  0.05

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of   is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally since the sample proportion is not given we will assume it to be

      \^ p = 0.5

Generally the sample size is mathematically represented as  

    n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>   n = [\frac{ 1.96 }{0.05} ]^2 *0.5 (1 - 0.5)

=>   n = 384

Generally the margin of error is mathematically represented as  

      E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

Generally if the level of confidence increases,  the critical value of  \frac{\alpha }{2}  increase and from the equation for margin of error we see the the critical  value varies directly with the margin of error , hence the margin of error  will increase also  

So  If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.

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The women'schorus has 33members. How many quartetscan be formed? How many singers will be left over?
andreyandreev [35.5K]

Answer: 8 quartets can be formed.

1 singer will be left over.

Step-by-step explanation:

A quartet is a group of 4 members.

Given: The women'schorus has 33 members.

The number of quartets can be formed = (Total members) divided by (4)

= 33 ÷ 4

By solving 33 ÷ 4  we get 8 as quotient and remainder as 1 such that

33 = 4 x 8 +1

Hence, 8 quartets can be formed.

1 singer will be left over.

8 0
3 years ago
What is the value of x?
artcher [175]
By Sine Rule,

x/sin30° = 8/sin90°

x/0.5 = 8/1

So x = 4.
8 0
3 years ago
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Convert Y = -7/2x-11 to Standard Form​
monitta

Answer:

7x + 2y = -22

Step-by-step explanation:

Standard form looks like Ax + By = C.

Start with Y = -7/2x-11.  Better to write that as Y = (-7/2)x - 11 to emphasize that the coefficient of x is the fraction -7/2.

Move the (-7/2)x term to the left:

(7/2)x + y = -11

Multiply all terms by 2 to eliminate the fractions:

7x + 2y = -22 (answer)

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a

Step-by-step explanation:

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Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow
Pavel [41]

Answer:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

Step-by-step explanation:

Data given and notation

\bar X_{1}=104 represent the mean for the sample 1

\bar X_{2}=106 represent the mean for the sample 2

\sigma_{1} =8.4 represent the population standard deviation for the sample 1

\sigma_{2}=7.6 represent the population standard deviation for the sample 2

n_{1}=80 sample size for the group 1

n_{2}=70 sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0:\mu_{1}-\mu_{2} =0

H1:\mu_{1} -\mu_{2} \neq 0

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)

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.

Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

7 0
3 years ago
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