Assume that a simple random sample has been selected from a

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternativehypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of 2.5g. a sample of 36 coins was collected. Those coins have a mean weight of 2.49482g and a standard deviation of 0.01393g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g. Do the coins appear to conform to the specifications of the coin mint?\"

a. H0: = 2.5g

H1:: 2.5g

b. H0: =2. 5g

    H1: 2.5g

c. H0: = 2. 5g

    H1:: < 2.5g

d   H0: 2.5g

     H1: = 2.5g

Identify the test statistic.

T= _______ Round to three decimal places as needed

Identify the P-value

The P-value is ________ Round to four decimal places as needed

State the final conclusion that addresses the original claim. Choose the correct answer below

a. Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

b. Reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

c. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

d. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

Do the coins appear to conform to the specifications of the coinmint?

a. Yes since the coins do not seem to come from a population with a mean weight different from 2.5

b. Yes, since the coins do not seem to come from a population with a mean weight different from 2.49482

c. No since the coins seem to come from a population with a mean weight different from 2.5

d. No, since the coins seem to come from a population with a mean weight different from 2.49482

e. The results are inconclusive because individual differences in coin weights need to be analyzed further.

a. H0: = 2.5g H1:: 2.5g	b. H0: =2. 5g     H1: 2.5g
c. H0: = 2. 5g     H1:: < 2.5g	d   H0: 2.5g      H1: = 2.5g

Solution

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternativehypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of 2.5g. a sample of 36 coins was collected. Those coins have a mean weight of 2.49482g and a standard deviation of 0.01393g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g. Do the coins appear to conform to the specifications of the coin mint?\"

a. H0: = 2.5g

H1:: 2.5g

b. H0: =2. 5g

    H1: 2.5g

c. H0: = 2. 5g

    H1:: < 2.5g

d   H0: 2.5g

     H1: = 2.5g

Identify the test statistic.

T= -2.231          Round to three decimal places as needed

Identify the P-value

The P-value is 0.0322          Round to four decimal places as needed

State the final conclusion that addresses the original claim. Choose the correct answer below

a. Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

b. Reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

c. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

d. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5g.

Do the coins appear to conform to the specifications of the coinmint?

a. Yes since the coins do not seem to come from a population with a mean weight different from 2.5

b. Yes, since the coins do not seem to come from a population with a mean weight different from 2.49482

c. No since the coins seem to come from a population with a mean weight different from 2.5

d. No, since the coins seem to come from a population with a mean weight different from 2.49482

e. The results are inconclusive because individual differences in coin weights need to be analyzed further.

EXcel output

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

2.5

Level of Significance

0.05

Sample Size

36

Sample Mean

2.49482

Sample Standard Deviation

0.01393

Intermediate Calculations

Standard Error of the Mean

0.0023

Degrees of Freedom

35

t Test Statistic

-2.2312

Two-Tail Test

Lower Critical Value

-2.0301

Upper Critical Value

2.0301

p-Value

0.0322

Reject the null hypothesis

a. H0: = 2.5g H1:: 2.5g	b. H0: =2. 5g     H1: 2.5g
c. H0: = 2. 5g     H1:: < 2.5g	d   H0: 2.5g      H1: = 2.5g