How many fifts are in 11

A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w

melamori03 [73]

Answer:

The hypothesis is:

H₀: $p_{X}-p_{Y}=0$ .

Hₐ: $p_{X}-p_{Y}$ .

Step-by-step explanation:

Let X = number of men who exercise regularly and Y = number of women who exercise regularly.

The information provided is:

$n_{X}=150\\X=88\\n_{Y}=200\\Y=130$

Compute the sample proportion of men and women who exercise regularly as follows:

$\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587$

$\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65$

The random variable X follows a Binomial distribution with parameters n = 150 and $\hat p_{X}=0.587$ .

The random variable Y also follows a Binomial distribution with parameters n = 200 and $\hat p_{Y}=0.65$ .

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\hat p=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

So, the sampling distribution of the proportion of men and women who exercise regularly follows a Normal distribution.

A two proportion z-test cab be performed to determine whether the proportion of women is more than men who exercise regularly.

The hypothesis for this test cab be defined as:

H₀: The proportion of women is same as men who exercise regularly, i.e. $p_{X}-p_{Y}=0$ .

Hₐ: The proportion of women is more than men who exercise regularly, i.e. $p_{X}-p_{Y}$ .

6 0

3 years ago

Read 2 more answers

Kedar earns a monthly salary of $2,200 plus a 3.75% commision on the amount of his sales at men's clothing store. What would he

Dmitriy789 [7]

Answer:

$2368.75

Step-by-step explanation:

Kedar earns a monthly salary of $2200 and a commission of 3.75%

He sold $4500 this month

The first step is to calculate his commission for this month

His commission can be calculated as follows

= 4500 × 3.75/100

= 4500 × 0.0375

= 168.75

Therefore yr amount earned this month can be calculated as follows

= 2200 + 168.75

= $2368.75

7 0

3 years ago

Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Consider the

Dafna1 [17]

Answer:

a) $\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

b) The 90% confidence interval would be given by (63.330;81.070)

$63.330 < \mu_{left}- \mu_{right}$

Step-by-step explanation:

1) Previous concepts and notation

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let put some notation

x=left arm , y = right arm

x: 175 169 182 146 144

y: 102 101 94 79 79

The first step is define the difference $d_i=x_i-y_i$ , that is given so we have:

d: 73, 68, 88, 67, 65

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,4)".And we see that $t_{\alpha/2}=2.13$