Question

0 Assume that a simple random sample has been selected from anomaly distributed population and to the given claim. Identify the rulindatemative hypotheses, les statisti, Palun, critical values and state the final conclusion that addresses the original cam A con ment has a specification that a particular con has a mean weight el 25g Asarrole of 34 coins was colected. Those coins have a mean weight of 248507g and a standard deviation of 0.01277g. Uw 0.06 significance over to test the claim that this sample is from a population with a man weight equal to 250 othecoins appear to conform to the specifications of the cont? H=250 H259 Identity the best - Round to three decimal places as needed.) Identify theorical values The critical s) ) (Pound to the decimal places as needed Use a comma to separate awwers as needed) Sate conclusion as the original claim. Choose the correct answer to O A Reject There is insufficient evidence to want rejection of the claim that the samples from a population with a mean wel 250 OB Foil to the There is insufficient evidence to wraction of the aim of the sample from a population with a mean weegto 25 OC Reject Hy There is sufficient evidence to warrant rejection of the claim that the samples from a population with a man weight at 250 OD. Fail to reject. There is sufficient evidence to wanatection of the claim that the sample is from a population with a new equal to 2.59 Do the consappear to conform to the specifications of the coin mind? OA No, since the coins soon to come from a population with a mean weight different from 2405079 OB. Yes, since the cor do not seem to come from a population wth a man weight different from 250 OC. Yes, since the coins do not seem to come from a population with a mean weight different from 24900V OD. No, no he coins son to come from a population with a man wat dierent from 259 OL Therests are inconclusive because individual diferences incoln we need to be analyred further Click to select your answers

Answer 1

Given

n = 34                      ( sample of 34 coins are collected )

$\bar{x}$ = 2.49507             ( sample coins have mean weight of 2.49507 g )

s = 0.01277              ( sample standard deviation is 0.01277 g )

To Test :-

H0 : $\mu$ = 2.5            ( sample coins come from a population with a mean weight of 2.5 g )

H1 : $\mu$ $\neq$ 2.5         ( sample coins may not come from a population with a mean weight of 2.5g )

{ Note that all options patterns are not visible in given image , so can't determine which option have correct above pattern }

Test statistics :-

TS =

T s/n

     =

2.49507 - 2.5 0.01277/134

TS = -2.251104

Hence , calculated test statistics value is TS = -2.251

To find critical value :-

Since alternative hypothesis is of "$\neq$" type , so these is two-taile t-test,and thus t-critical value will be given by

tala

Here
tala
is t-distributed with n-1 = 34-1 = 33 degree of freedom and $1596139398099_blob.png$ =0.05,

It can be computed from statistical book or more accurately from any software like R,Excel

From R

> qt(1-0.05/2,df=33)
[1] 2.034515

Thus = 2.035

tala

The critical value is 2.034

Rejection criteria :-

We reject null hypothesis is absolute value of calculated test statistics is greater than t-critical value

tala

i.e Reject H0 if | TS | >

tala

Here | TS | = | -2.251 | = 2.251 > 2.034              ( = 2.035 )

tala

Thus | TS | >

tala

So we reject null hypothesis at 0.05 level of significance .

Conclusion :-

We have sufficient evidence to reject the claim that this sample coins come from a population with a mean weight of 2.5 g

Hence correct option for conclusion is :-

Option C. Reject H0 , there is sufficient evidence to rejection of the claim that sample is from population with a mean weight equal to 2.5 g

Now since we have rejeted null hypothesis , so coins do not appears to confirm to the specification , since sample is from population with a mean weight different from 2.5 g

Hence correct option is

Option D. N0 , since the coins seems to be come from a population with a mean weight different from 2.5 g