A researcher claims that the proportion of people over 65 years of age in a certain city is 11%. To test this claim, a sample of 1000 people are taken and its determine that 126 people are over 65 years of age. The following is the setup for this hypothesis test: H0:p=0.11 Ha:p≠0.11 In this example, the p-value was determined to be 0.106. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to reject the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to reject the claim.

The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to reject the claim.

Step-by-step explanation:

We are given that a researcher claims that the proportion of people over 65 years of age in a certain city is 11%. To test this claim, a sample of 1000 people are taken and its determine that 126 people are over 65 years of age.

Let p = proportion of people over 65 years of age in a certain city = 11%

So, Null Hypothesis, : p = 0.11  {means that proportion of people over 65 years of age in a certain city is 11%}

Alternate Hypothesis, : p 0.11  {means that proportion of people over 65 years of age in a certain city is different from 11%}

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

                T.S. = ~ N(0,1)

where, = proportion of people over 65 years of age in a sample of 1000 people = = 0.126

           n = sample of people = 1000

So, test statistics =  

                            =  1.525

Now, we are given with the P-value and the significance level in the question;

P-value = 0.106 or 10.6%

Significance level = 5%

Our decision rule based on p-value is as follows;

Here, as we can clearly see that P-value is more than the significance level as 10.6% > 5%, so we have insufficient evidence to reject our null hypothesis.

Therefore, The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to reject the claim.

you need to show the graph

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: