Casey has a small business making dessert baskets. She estimates that her fixed weekly costs for rent, electricity, and salaries

Answer:

a) Null hypothesis:

Alternative hypothesis:

b)

Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c)

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

d)

Here again, with the p-value being less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

1) Provided data and references

represents the average of the samples

denotes the standard deviation of the samples

indicates the number of samples

is the value we are examining

defines the significance level for the test.

t represents the specific statistic of interest

indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis:

Alternative hypothesis:

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

(1)

Part b

In this scenario t=-2.3,

Initially, we need to calculate the degrees of freedom

Since this is a left-tailed test, the p-value is determined by:

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8,

We need to find the degrees of freedom

For the left-tailed test, the p-value is given by:

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6,

Firstly, we find the degrees of freedom

Since we are conducting a left-tailed test, the p-value is calculated as:

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

Response:

The width of the arch measures 105 meters

Detailed explanation:

The function that describes the width of the arch is

f(x) = -0.016(x - 52.5)² + 45

where x denotes the horizontal distance from the left end of the arch or the width at its base

f(x) indicates the vertical height of the arch

According to the given quadratic equation, the vertex coordinates of the parabola are (52.5, 45).

The vertex coordinates indicate that

the arch's height is 45 meters

and half the horizontal span from the left end is 52.5 meters

Therefore, the bridge's total width is calculated as 2 times the half span from the left side, which is 2 × 52.5

resulting in 105 meters

Consequently, the bridge's width is 105 meters.

Response: A on edg 2021

Detailed breakdown: