A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be,

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 goat population will reach 1000 in a time span of 12.4 years

Detailed explanation:

After t years, the population of goats is described by

where indicates the initial count of goats and b is the growth rate per capita.

Based on the problem,

• 
• b = 0.5
• N = 1000

To determine how many 3/64 gallon servings can be filled from a total of 2/3 gallon of punch, perform the division of 2/3 by 3/64. The outcome is not a whole number, but this method illustrates the solution. Vinny's total is 2/3 of a gallon of punch, with each guest receiving a measure of 3/64 gallon, which tells us how many can be accommodated by performing<span> (2/3) / (3/64).</span>

The likelihood of all sprinklers functioning properly in a fire stands at 0.0282. This was determined via the Binomial probability distribution since the activation of sprinklers occurs independently. There are two potential outcomes: they either function correctly or they do not. The binomial distribution is used to calculate the probabilities over multiple trials. The resulting equation b(x; n, P) = P(X=x) considers the number of successes, probability of success in a singular attempt, and the number of trials involved. The computations conclude with the probability being reflected as 0.0282.