The difference between 22 and x

In a sample of nequals16 lichen specimens, the researchers found the mean and standard deviation of the amount of the radioacti

Dovator [93]

Answer:

(a) The confidence level desired by the researchers is 95%.

(b) The sampling error is 0.001 microcurie per millilitre.

(c) The sample size necessary to obtain the desired estimate is 36.

Step-by-step explanation:

The mean and standard deviation of the amount of the radioactive element, cesium-137 present in a sample of n = 16 lichen specimen are:

$\bar x=0.009\\s=0.003$

Now it is provided that the researchers want to increase the sample size in order to estimate the mean μ to within 0.001 microcurie per millilitre of its true value, using a 95% confidence interval.

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x \pm z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

(a)

The confidence level is the probability that a particular value of the parameter under study falls within a specific interval of values.

In this case the researches wants to estimate the mean using the 95% confidence interval.

Thus, the confidence level desired by the researchers is 95%.

(b)

In case of statistical analysis, during the computation of a certain statistic, to estimate the value of the parameter under study, certain error occurs which are known as the sampling error.

In case of the estimate of parameter using a confidence interval the sampling error is known as the margin of error.

In this case the margin of error is 0.001 microcurie per millilitre.

(c)

The margin of error is computed using the formula:

$MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size value as follows:

$MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times s}{MOE}]^{2}$

$=[\frac{1.96\times 0.003}{0.001}]^{2}$

$=34.5744\\\approx36$

Thus, the sample size necessary to obtain the desired estimate is 36.

8 0

3 years ago

Which function below is the inverse of f(x)=7x-1/2

Margaret [11]

We write f(x) in terms of y I.e y=7x-1/2.

Fractions are sometimes ambiguous, we eliminate the fraction by multiplaying the entire function by 2.so as to get 2y=14x-1.

Make x the subject, x=2y+1/14,

Thus the inverse f(x)=2x+1/14

5 0

3 years ago

HELP!!!!!!!!

zhannawk [14.2K]

ANSWER

(Choice A)

-4(3e+4)

EXPLANATION

The given expression is

$- 7 + 3( - 4e - 3)$

We expand to get:

$- 7 - 12e - 9$

We regroup the terms to get:

$- 12e - 9 - 7$

Simplify now to get:

$- 12e - 16$

We now factor -4 to obtain:

$- 4(3e + 4)$

The correct choice is A.

3 0

3 years ago

Read 2 more answers

The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2300 employees at its Sam's Club warehouse unit

Advocard [28]

Answer:

(a) The mean is 52 and the median is 55.

(b) The first quartile is 44 and the third quartile is 60.

(c) The value of range is 33 and the inter-quartile range is 16.

(d) The variance is 100.143 and the standard deviation is 10.01.

(e) There are no outliers in the data set.

(f) Yes

Step-by-step explanation:

The data provided is:

S = {55, 56, 44, 43, 44, 56, 60, 62, 57, 45, 36, 38, 50, 69, 65}

(a)

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum x\\=\frac{1}{15}[55+ 56+ 44+ 43+ 44+ 56+ 60+ 62+ 57+ 45 +36 +38 +50 +69+ 65]\\=\frac{780}{15}\\=52$

Thus, the mean is 52.

The median for odd set of values is the computed using the formula:

$Median=(\frac{n+1}{2})^{th}\ obs.$

Arrange the data set in ascending order as follows:

36, 38, 43, 44, 44, 45, 50, 55, 56, 56, 57, 60, 62, 65, 69

There are 15 values in the set.

Compute the median value as follows:

$Median=(\frac{15+1}{2})^{th}\ obs.=(\frac{16}{2})^{th}\ obs.=8^{th}\ observation$

The 8th observation is, 55.

Thus, the median is 55.

(b)

The first quartile is the middle value of the upper-half of the data set.

The upper-half of the data set is:

36, 38, 43, 44, 44, 45, 50

The middle value of the data set is 44.

Thus, the first quartile is 44.

The third quartile is the middle value of the lower-half of the data set.

The upper-half of the data set is:

56, 56, 57, 60, 62, 65, 69

The middle value of the data set is 60.

Thus, the third quartile is 60.

(c)

The range of a data set is the difference between the maximum and minimum value.

Maximum = 69

Minimum = 36

Compute the value of Range as follows:

$Range =Maximum-Minimum\\=69-36\\=33$

Thus, the value of range is 33.

The inter-quartile range is the difference between the first and third quartile value.

Compute the value of IQR as follows:

$IQR=Q_{3}-Q_{1}\\=60-44\\=16$

Thus, the inter-quartile range is 16.

(d)

Compute the variance of the data set as follows:

$s^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=\frac{1}{15-1}[(55-52)^{2}+(56-52)^{2}+...+(65-52)^{2}]\\=100.143$

Thus, the variance is 100.143.

Compute the value of standard deviation as follows:

$s=\sqrt{s^{2}}=\sqrt{100.143}=10.01$

Thus, the standard deviation is 10.01.

(e)

An outlier is a data value that is different from the remaining values.

An outlier is a value that lies below 1.5 IQR of the first quartile or above 1.5 IQR of the third quartile.

Compute the value of Q₁ - 1.5 IQR as follows:

$Q_{1}-1.5QR=44-1.5\times 16=20$

Compute the value of Q₃ + 1.5 IQR as follows:

$Q_{3}+1.5QR=60-1.5\times 16=80$

The minimum value is 36 and the maximum is 69.

None of the values is less than 20 or more than 80.

Thus, there are no outliers in the data set.

(f)

Yes, the data provided indicates that the Walmart is meeting its goal for reducing the number of hourly employees

6 0

3 years ago

A florist has 54 white roses, 72 red roses, and 108 pink roses. If he makes the greatest number possible of identical bouquets u

drek231 [11]

Find the greatest common factor of each flower:

White roses = 54 = 1, 2 , 3, 6, 9, 18, 27, 54

Red roses = 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Pink roses = 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The common factors of all three are: 1, 2, 3, 6, 9, 18.

The greatest common factor is 18, so he can make 18 bouquets.

Divide the total red roses by 18:

72 / 18 = 4

There will be 4 red roses in each bouquet.

7 0

3 years ago