Will mark brainliest has to be correct.

A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample stand

Tpy6a [65]

Answer:

We conclude that the population mean is different from 10.5.

Step-by-step explanation:

We are given that a random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2.

<em>We have to test the claim that the population mean is 10.5.</em>

Let, NULL HYPOTHESIS, $H_0$ : $\mu$ = 10.5 {means that the population mean is 10.5}

ALTERNATE HYPOTHESIS, $H_a$ : $\mu \neq$ 10.5 {means that the population mean is different from 10.5}

The test statistics that will be used here is One-sample t-test;

T.S. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 11

s = sample standard deviation = 2

$\mu$ = population mean

n = sample of values = 16

So, <u>test statistics</u> = $\frac{11-10.5}{\frac{2}{\sqrt{16} } }$ ~ $t_1_5$

= 1

<em>Now, at 0.05 significance level, t table gives a critical value of 2.131 at 15 degree of freedom. Since our test statistics is way less than the critical value of t so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.</em>

Therefore, we conclude that the population mean is different from 10.5.

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4 years ago

PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has th

Svetlanka [38]

A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14

<h3>What is a polynomial function?</h3>

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

x= -2, x=7

Given,

P(x) = 0

This polynomial function has the roots,

x= -2, x=7

So,

(x+2)(x-7)

We have to multiply both of them we get,

P(x)=(x+2)(x-7)

0=x²-5x-14

x²-5x-14=0

Therefore, P(x)=x²-5x-14 is the polynomial function.