Significance test to see if this holds true in her nation. She takes a random sample of babies and observes a mean birthweight of \bar x=3.43\text{ kg.} x ˉ =3.43 kg. x, with, \bar, on top, equals, 3, point, 43, start text, space, k, g, point, end text Here's Marta's null hypothesis: H_0:H 0 :H, start subscript, 0, end subscript, colon The mean birth weight in this nation is...

Option D is correct.

H₀: The mean birth weight in this nation is equal to 3.5 kg

Step-by-step explanation:

In Hypothesis testing, involving testing two data set, the null hypothesis is the one always playing Devil's advocate and saying that there isn't any 'significant' difference between the two datasets being compared.

It usually has the signs =, ≤ and ≥, indicating truly that there isn't a significant difference between a true value and one obtained from a set of sample. It is always preaching that the value obtained from the sample is basically not different from the true value.

So, for this question, the true value is the widely known, European average birthweight (3.50 kg). A value obtained from a simple random sample, is then tested to see how different or similar it is is to the true, widely known average birth weight.

The obtained sample mean, μ₀ is then stated to not be significantly different from the widely known average birth weight. This is the null hypothesis.

H₀: μ₀ = 3.5 kg

This is what is now tested statistically, if the p-value exceeds the significance level, we do not reject the null hypothesis and we conclude that there isn't truly a significant difference in the sample mean obtained and the population mean of 3.5 kg.

When the p-value is lesser than the significance level, we promptly reject the the null hypothesis. This is where the alternative hypothesis, which is basically saying the direct opposite of what the null hypothesis is saying, comes in.

The alternative hypothesis has inequality signs such as ≠, < and >, to indicate that there is indeed a significant difference between the two quantities being tested.

Hₐ: μ₀ ≠ 3.5 kg or more specifically,

Hₐ: μ₀ < 3.5 kg

Basically, the major takeaway from this question is that it is the population mean that usually/normally appear in the hypothesis statements.

Hope this Helps!!!

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be