Question

Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.025 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation? Cents portion of check | 0-24 | 25-49 | 50-74 | 75-99 Number | 63 | 17 | 9 | 11 Click here to view the chi-square distribution table. The test statistic is . (Round to three decimal places as needed.) The critical value is . (Round to three decimal places as needed.) State the conclusion. H0. There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results to support the expectation that the frequency for the first category is disproportionately high.

          Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.
A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.025 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation?

Cents portion of check | 0-24 | 25-49 | 50-74 | 75-99
Number | 63 | 17 | 9 | 11

Click here to view the chi-square distribution table.

The test statistic is .
(Round to three decimal places as needed.)

The critical value is .
(Round to three decimal places as needed.)

State the conclusion.

H0. There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results to support the expectation that the frequency for the first category is disproportionately high.

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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.
A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.025 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation?

Cents portion of check | 0-24 | 25-49 | 50-74 | 75-99
Number | 63 | 17 | 9 | 11

Click here to view the chi-square distribution table.

The test statistic is .
(Round to three decimal places as needed.)

The critical value is .
(Round to three decimal places as needed.)

State the conclusion.

H0. There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results to support the expectation that the frequency for the first category is disproportionately high.

Added by Mark A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Adi S

09/16/2023

Step 1

Define the null hypothesis (H₀) and the alternative hypothesis (H₁): H₀: The four categories are equally likely. H₁: The four categories are not equally likely. Show more…

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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.025 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation? Cents portion of check | 0-24 | 25-49 | 50-74 | 75-99 Number | 63 | 17 | 9 | 11 The test statistic is . (Round to three decimal places as needed.) The critical value is . (Round to three decimal places as needed.) State the conclusion. H0. There sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results to support the expectation that the frequency for the first category is disproportionately high.

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Transcript

00:01 So, null hypothesis here h0 here the 4 categories, the 4 categories, the 4 categories are equally likely, are equally, are equally likely, are equally likely and here the alternative hypothesis here is h0 here the 4 categories, the 4 categories, the 4 categories are not equally likely, are not equally likely, are not equally likely, not equally likely.

00:46 Now here we have to set the significance level so here the alpha here that is equal to 0 .025 is given and here we have to calculate the expected frequency so here expected frequency we have to calculate, expected frequency so here now if the 4 categories are equally likely equally likely each category should have an equal proportion of the total number of checks so here since, since there are, since there are 100 checks in total, 100 checks in total, in total each category would expected to have that is here 100 divided by 4 and so it is equal to 25 checks now here we have to calculate the c square test statistic here the formula for c square test here c square test statistic, statistic here for the goodness of the test that is x square here that is equal to the summation of observed frequency minus the expected frequency whole square and here whole divided by that is the expected frequency.

02:31 Now here that is equal to here that is 63 minus 25 whole square plus 63 minus 25 whole square divided by expected frequency that is 25 plus now here 17 minus 25 whole square divided by 25 plus here that is 9 minus 25 whole square divided by 25 plus 11 minus 25 whole square divided by 25 and now here that is equal to here that is 24 .96, 24 .96, 0 is the rounded to 3 decimal places now here calculate here that is since, since there are 4 categories, since there are 4 categories here 2 here that is a degree of freedom degree of freedom is 4 minus 1 that is equal to 3.

03:41 Now for check 3 for the c square now we are using, using the significance level that is alpha that is equal to 0 .025 and the degree of freedom here that is equal to 3.

03:56 We find that, we find that, find that, find the critical value, the critical value, the critical value to be here that is approximately here that is 7 .815 rounded to 3 decimal places...

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