The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is .

p-value = 0.0458

Step-by-step explanation:

We are given sample size; n = 30

Variance = 0.027

Standard deviation; S = 0.2

The value we want to test will be given by;

σ_o = √var = √0.027 = 0.1643

α = significance level

Before we test the hypothesis, let's calculate the statistic given by;

t = (n-1)[s/σ_o]²

So, t = (30 - 1)[0.2/0.1643]² = 42.972

Now, let's state the hypothesis ;

H1; σ ≤ 0.027

H0; σ > 0.027

The statistic has a Chi Square distribution distribution with degree of freedom as (n - 1). Thus,

The degree of freedom is,

n - 1 = 30 - 1 = 29

Using a chi square calculator online, P-value with chi square of 42.972 and degree of freedom as 29, p = 0.0458

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

step-by-step explanation: