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2 years ago

Please help me....))

Mathematics

1 answer:

miskamm [114]2 years ago

8 0

The first picture is for number 1 and the second one for number 2.

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The local public transport authority is conducting research into commuter behaviour. A previous census indicated that the mean c

kondor19780726 [428]

Answer:

$H_0:\mu = 45$ and $H_a:\mu < 45$

$T = 34.88$

The null hypothesis is not rejected

Step-by-step explanation:

Given

Random sample of 50 commuter times

Solving (a): The null and alternate hypothesis

From the question, a previous census shows that:

$\mu =45$ and $\sigma= 9.1$

This is the null hypothesis i.e.

$H_0:\mu = 45$

Reading further, a new test was to show whether the average has decreased.

This is the alternate hypothesis, and it is represented as:

$H_a:\mu < 45$

Solving (b) and (c): The test statistic (T).

This is calculated using:

$T = \frac{\mu}{\sigma/\sqrt n}$

In this case:

$n = 50$ $\mu =45$ and $\sigma= 9.1$

So:

$T = \frac{45}{9.1/\sqrt{50}}$

$T = \frac{45}{9.1/7.07}$

$T = \frac{45}{1.29}$

$T = 34.88$

Solving (c): Accept or reject null hypothesis

$\alpha = 0.05$

First calculate the degrees of freedom (df)

$df = n - 1 = 50 - 1$

$d f = 49$

From the t distribution table,

At: $d f = 49$ , $\alpha = 0.05$ and $T = 34.88$

the t score is:

$p = 1.676$

$p > 0.05$

So, the null hypothesis is not rejected

7 0

2 years ago

मिनधन १.. 18,900 हुन्छ भन सावा रकम पता लगा

Vladimir [108]

Answer:

Solution given:

principal [P]=P

time [T]=4 years

Rate [R]=13%

compound amount=18900

Simple interest=P-18900

we have

simple interest= $\frac{P*T*R}{100}$

P-18900= $\frac{P*4*13}{100}$

100P-1890000=52P

48P=1890000

P=1890000/48

P=39375

the sum that amounts =Rs 39375

5 0

2 years ago

Which of the following facts would be sufficient to

Nady [450]

[email protected] = bainegoudy666 the answer is abbca

4 0

3 years ago

Paige and Cindy have been saving money. Paige started with $350 in her savings and deposits $25 into her savings each week. Cind

LUCKY_DIMON [66]

Answer:

D. 11

Step-by-step explanation:

T = total savings

w = number of weeks

Paige:

T = 350 + 25w

Cindy:

T = 190 + 40w

In how many weeks will Cindy have more money in her savings than Paige

Equate the total savings of both of them

350 + 25w = 190 + 40w

Collect like terms

350 - 190 = 40w - 25w

160 = 15w

w = 160/15

w = 10.67

Approximately,

In 11 weeks, will Cindy have more money in her savings than Paige

Check:

Paige:

T = 350 + 25w

= 350 + 25(11)

= 350 + 275

= 625

Cindy:

T = 190 + 40w

= 190 + 40(11)

= 190 + 440

= 630

3 0

2 years ago

#10 i The table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each the pa

lions [1.4K]

The line of best fit is a straight line that can be used to predict the

average daily attendance for a given admission cost.

Correct responses:

The equation of best fit is; $\underline{ \hat Y = 1,042 - 4.9 \cdot X_i}$

The correlation coefficient is; r ≈ -0.969

<h3>Methods by which the line of best fit is found</h3>

The given data is presented in the following tabular format;

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|}Cost, (dollars), x&20&21&22&24&25&27&28&30\\Daily attendance, y&940&935&940&925&920&905&910&890\end{array}\right]$

The equation of the line of best fit is given by the regression line

equation as follows;

$\hat Y = \mathbf{b_0 + b_1 \cdot X_i}$

Where;

$\hat Y$ = Predicted value of the ith observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

$X_i$ = The ith observed value

$b_1 = \mathbf{\dfrac{\sum (X - \overline X) \cdot (Y - \overline Y) }{\sum \left(X - \overline X \right)^2}}$

$\overline X$ = 24.625

$\overline Y$ = 960.625

$\mathbf{\sum(X - \overline X) \cdot (Y - \overline Y)} = -433.125$

$\mathbf{\sum(X - \overline X)^2} = 87.875$

Therefore;

$b_1 = \mathbf{\dfrac{-433.125}{87.875}} \approx -4.9289$

Therefore;

The slope given to the nearest tenth is b₁ ≈ -4.9

$b_0 = \mathbf{\dfrac{\left(\sum Y \right) \cdot \left(\sum X^2 \right) - \left(\sum X \right) \cdot \left(\sum X \cdot Y\right)} {n \cdot \left(\sum X^2\right) - \left(\sum X \right)^2}}$

By using MS Excel, we have;

n = 8

∑X = 197

∑Y = 7365

∑X² = 4939

∑Y² = 6782675

∑X·Y = 180930

(∑X)² = 38809

Therefore;

$b_0 = \dfrac{7365 \times 4939-197 \times 180930}{8 \times 4939 - 38809} \approx \mathbf{1041.9986}$

The y-intercept given to the nearest tenth is b₀ ≈ 1,042

The equation of the line of best fit is therefore;

$\underline{\hat Y = 1042 - 4.9 \cdot X_i}$

The correlation coefficient is given by the formula;

$\displaystyle r = \mathbf{\dfrac{\sum \left(X_i - \overline X) \cdot \left(Y - \overline Y \right)}{ \sqrt{\sum \left(X_i - \overline X \right)^2 \cdot \sum \left(Y_i - \overline Y \right)^2} }}$