Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. De

Answer:

The P-value ranges between 2.5% and 5% according to the t-table.

Step-by-step explanation:

A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.

Let = true average age of all students at the university.

So, the Null Hypothesis, : 24 years {indicating the average age is less than or equal to 24 years}

Alternate Hypothesis, : > 24 years {indicating the average age is significantly greater than 24 years}

Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;

                              T.S. = ~

where, = sample average age = 25 years

             s = sample standard deviation = 2 years

             n = sample size = 16

This gives us the test statistics = ~

                                     = 2

The value of the t-test statistics is 2.

Moreover, the P-value of the test-statistics can be found as follows;

P-value = P( > 2) = 0.034 {as per the t-table}

Thus, the P-value lies between 2.5% and 5% based on the t-table.

The equation representing the circle centered at (-27, 120) that passes through the origin is:

Solution:

The general equation of a circle is expressed as:

Where,

(a, b) denotes the center of the circle

r signifies the radius

Given the center as (-27, 120)

Thus;

a = -27

b = 120

Considering it intersects the origin, meaning (x, y) = (0, 0)

Substituting (a, b) = (-27, 120) and (x, y) = (0, 0) into the equation

Input = 15129 and (a, b) = (-27, 120) into the equation

Hence, the equation characterizing the circle is determined