Which steps could be used to solve this story problem?

The following 5 questions are based on this information: An economist claims that average weekly food expenditure of households

liq [111]

Answer:

Null hypothesis: $\mu_{1}-\mu_{0}\leq 0$

Alternative hypothesis: $\mu_{1}-\mu_{2}>0$

$SE=\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}=2.705$

b) 2.70

$t=\frac{(164-159)-0}{\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}}=1.850$

b. 1.85

$p_v =P(Z>1.85)=0.032$

b. 0.03

a. We can reject H(0) in favor of H(a)

Step-by-step explanation:

Data given and notation

$\bar X_{1}=164$ represent the mean for the sample 1

$\bar X_{2}=159$ represent the mean for the sample 2

$\sigma_{1}=12.5$ represent the population standard deviation for the sample 1

$s_{2}=9.25$ represent the population standard deviation for the sample B2

$n_{1}=35$ sample size selected 1

$n_{2}=30$ sample size selected 2

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the expenditure of households in City 1 is more than that of households in City 2, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{0}\leq 0$

Alternative hypothesis: $\mu_{1}-\mu_{2}>0$

We know the population deviations, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-0}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

t-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".

Standard error

The standard error on this case is given by:

$SE=\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}$

Replacing the values that we have we got:

$SE=\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}=2.705$

b. 2.70

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{(164-159)-0}{\sqrt{\frac{12.5^2}{35}+\frac{9.25^2}{30}}}=1.850$

P-value

Since is a one side right tailed test the p value would be:

$p_v =P(Z>1.85)=0.032$

b. 0.03

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

a. We can reject H(0) in favor of H(a)

4 0

3 years ago

3y + 7 = x is this a direct proportion

Tju [1.3M]

Answer:

no

Step-by-step explanation:

if the ratio (yx) of two variables (x and y) is equal to a constant (k=yx) .in this case y is said to be directly proportional to x with proportionality constant k

3 0

2 years ago

Ted knows the actual distance between two cities is 150 miles. His map shows a distance of 2 inches between these cities. What i

Serjik [45]

Answer:

The scale used on his map is 150 miles : 2 inches.

Step-by-step explanation:

Given:

Ted knows the actual distance between two cities is 150 miles. His map shows a distance of 2 inches between these cities.

Now, to find the scale Ted used on his map.

The actual distance Ted know between two cities = 150 miles.

The distance on map between these cities = 2 inches.

So, to get the scale used on his map:

$\frac{The\ actual\ distance\ Ted\ know\ between\ two\ cities}{The\ distance\ on\ map\ between\ these\ cities}$

$=\frac{150\ miles}{2\ inches}$

$=150\ miles:2\ inches.$

Therefore, the scale used on his map is 150 miles : 2 inches.

5 0

2 years ago

The three factors that must exist for a person to commit fraud include

Nimfa-mama [501]

Answer:

(1) Opportunity, (2) Pressure, and (3) Rationalization must exist for a person to commit fraud.

Important to Note:

Pressure is sometimes referred to as motivation or incentive.

Rationalization is sometimes called justification or attitude.

7 0

2 years ago

Determine if there is a proportional relationship between the two quantities

Shalnov [3]

Answer:

The table a not represent a proportional relationship between the two quantities

The table b represent a proportional relationship between the two quantities

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Verify each table

Table a

Let

A ----> the independent variable or input value

B ----> the dependent variable or output value

the value of k will be

$k=\frac{B}{A}$

For A=35, B=92 ---> $k=\frac{92}{35}=2.63$

For A=23, B=80 ---> $k=\frac{80}{23}=3.48$

the values of k are different

therefore

There is no proportional relationship between the two quantities

Table b

Let

C ----> the independent variable or input value

D ----> the dependent variable or output value

the value of k will be

$k=\frac{D}{C}$

For C=20, D=8 ---> $k=\frac{8}{20}=0.40$

For C=12.5, D=5 ---> $k=\frac{5}{12.5}=0.40$

the values of k are equal

therefore

There is a proportional relationship between the two quantities

The linear equation is equal to

$D=0.40C$

7 0

3 years ago