Question

Determine the value of the t test statistic. (Use decimal notation. Give your answer to two decimal places.) The results of a major city's restaurant inspections are available through its online newspaper. Critical food violations are those that put patrons at risk of getting sick and must be immediately corrected by the restaurant. An SRS of n = 300 inspections from more than 10,000 inspections since January 2012 had the sample mean x = 0.90 violations and the sample standard deviation s = 2.35 violations. t= Incorrect Determine the P-value. (Use decimal notation. Give your answer to four decimal places. If you use Table D, give the closest lower boundary.) P-value = Incorrect

Answer 1

The equation of the parabola that opens to the left, with a vertex at (2,7) and a focal diameter of 12 is: \((y - 7)^2 = -48(x - 2)\).

Step-by-step explanation:

A parabola opening to the left has its focus to the left of the vertex. The standard form of the equation for a parabola with a horizontal axis is \((y - k)^2 = 4p(x - h)\), where \((h, k)\) is the vertex and \(p\) is the distance between the vertex and the focus.

Given the vertex at (2,7) and a focal diameter of 12, the focal width is 12, meaning the distance from the vertex to the focus (or from the vertex to the directrix) is \(p = \frac{12}{2} = 6\).

Since the parabola opens to the left, the focus is 6 units to the left of the vertex. Therefore, the focus is at (-4, 7). Using the formula \(4p = \text{focal width}\), we find \(4p = 12\) and thus, \(p = 3\).

Substituting the vertex (2,7) and the value of \(p\) into the equation gives \((y - 7)^2 = -48(x - 2)\), where the negative sign before \(48\) indicates the parabola opens to the left.

Answer 2

The value of the t test statistic is approximately 4.98.

To find the t test statistic, we can use the following formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

In this case, we don't have a specific hypothesized mean to test against, so we'll use the sample mean itself as a placeholder to calculate the t statistic. This approach will provide a measure of how much the sample mean deviates from zero in terms of standard errors.

Plugging in the given values:

t = (0.90 - 0) / (2.35 / √300)

t ≈ 4.98