Brainliest to first!! Pls help!! :)

The Municipal Transit Authority wants to know if, on weekdays, more passengers ride the northbound blue line train towards the c

Kitty [74]

Answer:

The 90% confidence interval $-49.8$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 < \mu_2$

The distribution test statistics is $t = -3.222$

The rejection region is p-value < $\alpha$

The decision rule is reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that there are more passengers riding the 8:30 train

The p-value is $p-value =0.000951$

Step-by-step explanation:

From the question we are told that

The first sample size $n_1 = 30$

The first sample mean is $\= x _1 = 323$

The first standard deviation is $s_1 = 41$

The second sample size is $n_2 = 45$

The second sample mean is $\=x_2 = 356$

The second standard deviation is $s_2 = 45$

given that the confidence level is 90% then the level of significance is mathematically represented as

$\alpha = (100 -90)\%$

$\alpha = 0.10$

Generally the critical value of $\frac{\alpha }{2}$ obtained from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the pooled variance is mathematically represented as

$s^2 = \frac{(n_1 - 1)s_1^2 + (n_2 -1)s_2^2 }{n_1 + n_2 -2}$

$s^2 = \frac{(30 -1)(41^2) + (45-1)45^2}{30+45 -2}$

$s^2 = 1888.34$

Generally the standard error is mathematically represented as

$SE = \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2} }$

=> $SE = \sqrt{\frac{1888.34}{30} + \frac{1888.34}{45} }$

=> $SE = 10.24$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * SE$

$E = 1.645* 10.24$

$E = 16.85$

Generally the 90% confidence interval is mathematically represented as

$\=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E$

$323 -356 -16.84$

$-49.8$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 < \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \=x_2 }{SE}$

=> $t = \frac{323-356}{10.24}$

=> $t = -3.222$

Generally the degree of freedom is mathematically represented as

$df = n_1+n_2 -2$

$df = 30 + 45 -2$

$df = 73$

The p-value is obtained from the student t distribution table at degree of freedom of 73 at 0.05 level of significance

The value is $p-value =0.000951$

Here the level of significance is $\alpha = 5\% = 0.05$

Given that the p-value < $\alpha$ then we reject the null hypothesis

Then the conclusion is

There is sufficient evidence to conclude that there are more passengers riding the 8:30 train

5 0

3 years ago

The incenter is the center of the________ of a triangle.

Usimov [2.4K]

Answer: Angle bisectors

Step-by-step explanation:

The incenter is the point forming the origin of a circle inscribed inside the triangle. Like the centroid, the incenter is always inside the triangle. It is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle.

5 0

3 years ago

Read 2 more answers

G = {(5,3), (2, 3), (6,4)} Is G^-1 a function and why?

sleet_krkn [62]

Answer:

The inverse relation G^(-1) is not a function. Why not? Because the y value y = 3 is paired up with more than one x value (x = 5, x = 2). The inverse relation G^(-1) is the set shown below

{(3,5), (3,2), (4,6)}

All I've done is swap the (x,y) values for each ordered pair to form the inverse relation. As you can see, x = 3 leads to multiple y value outputs which is why this relation is not a function. So in short, the answer is choice C. To have the inverse relation be a function, each value in the original domain must map to exactly one value in the range only. However that doesn't happen as the domain values map to an overlapping y value (y = 3).

5 0

3 years ago

What fraction of a year are 31 days ?

Alborosie

9514 1404 393

Answer:

non-leap years: 31/365
leap years: 31/366

Step-by-step explanation:

As a fraction of the number of days in a calendar year, it will depend on whether the year is a leap year.

non-leap years have 365 days, so 31 days is 31/365 years.

leap years have 366 days, so 31 days is 31/366 years.

_____

If you're asking for the purpose of computing interest, you need to be aware that "ordinary interest" counts 360 days in a year. 31 days would be 31/360 years. "Exact interest" counts 365 days in a year, so 31 days would be 31/365 years.

In astronomy, the definitions of "day" and "year" may vary, depending on the frame of reference and what direction in space marks the boundary of the period. The precise fraction will depend on how you define these terms and where the clock is located.

5 0

3 years ago

After 10 months the simple interest of a 6,000 investment was $769. What is the interest rate

slega [8]

Answer:

Interest rate ( r ) = 15.38% or 0.1538

Step-by-step explanation:

Given the principal (P) = $6,000, and the simple interest of $769 earned after 10 months:

We can determine the interest rate (r ) by creating its formula algebraically, then use the equation to solve for its value.

Using the simple interest formula,

I = P × r × t 

where:

I = interest amount = $769

P = present value of the principal = $6,000

r = interest rate

t = time = 10/12 (10 months out of 12 months) = 0.83333

I = P × r × t

Divide both sides by P × t:

I / ( P × t ) = P × t × r / ( P × t )

I / ( P × t ) = r

Therefore, the formula for the interest rate is: r = I / ( P × t )

Substitute the given values into the formula to solve for r:

r = I / ( P × t )

r = $769 / ($6,000 × 0.83333)

r = $769/ 4,999.99999

r = 0.1538 or 15.38%

I'd greatly appreciate it if you could please mark my answers as the Brainliest, if you find this solution helpful :)

8 0

2 years ago