A telephone survey of 1000 randomly selected us adults found that 31% of them say they believe in ghosts.14 does this provide evidence that more than 1 in 4 us adults believe in ghosts? clearly show all details of the test. lock, robin h.; lock, patti frazer; morgan, kari lock; lock, eric f.; lock, dennis f.. statistics: unlocking the power of data, 2nd edition (page 418). wiley. kindle edition.

H₀ proportion = 0.25

Hₐ : p ≠ 0.25

z test = 4.38178

Probability = 0.00001177 low, therefore

Yes,  more than 0.25 believe in ghosts

Explanation:

Here we have

H₀ : p = 0.25

Hₐ : p ≠ 0.25

We derive the test statistic as follows

Where:

= Sample proportion = X/n = 31% or 0.31

n = Sample size = 1000

p = Population proportion = 0.25

q = 1 - p

α = 5%

Plugging the values, we have,

From which the probability is looked up to be 0.00001177

Whereby as 5% confidence level the critical z = ± 1.96

Therefore, whereby p ≈ 0 <α = 0.05 we reject the null hypothesis, that is there is sufficient statistical evidence that more than 1 in 4 us adults believe in ghost.

marginal cost is a microeconomic measure that us to evaluate the extent to which the level of production of a good is sustainable in accounting, that is, to how many quantities the company plans to profit from the production of the good.

the concept of marginal cost is simple, it means the cost of producing one more item. for example, in the case of pies, the marginal cost is the cost of producing one more pie than those that have already been produced.

it is important to understand that productive activity influences marginal cost. the marginal cost of some goods can be very high, while others may be insignificant. for example, the marginal cost of producing an extra plane is very high. already the marginal cost of a water company to provide 1l more water is derisory.

in the case of pies, the cost involves the inputs, the labor and the fixed cost, which involves the fixed space of the bakery. the level of production initially has the marginal cost decreasing because there is space and manpower available. however, to produce more you have to hire more workers and buy more inputs. if physical space is limited, workers will conflict with places, inputs and their productivity will decrease, meaning there is an optimum point of production for each level of space and manpower. from this point on, the productivity of the workers will be getting smaller because of lack of space, so that the marginal cost of producing one more pie will be increasing. so, although you have not posted the chart, but if you have the answer, you can see that my explanation goes according to the marginal cost curve that will increase from the 4th pie, answer (c).