Question

A police department released the numbers of calls for the different days of the week during the month of​ October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis? Day nbsp Sun Mon Tues Wed Thurs Fri Sat Frequency 157 207 222 247 175 205 230 Determine the null and alternative hypotheses. Upper H 0​: ▼ Police calls occur with the same frequency on the different days of the week. Police calls occur with all different frequencies on the different days of the week. At least two days have a different frequency of calls than the other days. At least one day has a different frequency of calls than the other days. Upper H 1​: ▼ At least two days have a different frequency of calls than the other days. Police calls occur with the same frequency on the different days of the week. At least one day has a different frequency of calls than the other days. Police calls occur with all different frequencies on the different days of the week. Calculate the test​ statistic, chi squared. chi squaredequals nothing ​(Round to three decimal places as​ needed.) Calculate the​ P-value. ​P-valueequals nothing ​(Round to four decimal places as​ needed.) What is the conclusion for this hypothesis​ test? A. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls. B. Fail to reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls. C. Reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls. D. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis? A. Because October has 31​ days, each day of the week occurs the same number of times as the other days of the week. B. Because October has 31​ days, three of the days of the week occur more often than the other days of the week. C. Because October has 31​ days, one of the days of the week occur more often than the other days of the week. D. Because October has 31​ days, two of the days of the week occur more often than the other days of the week.

Answer 1

Category	Observed (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Sun	157	1/7	1443 * 1/7= 206.142857	(157 - 206.142857)²/206.142857 = 11.7153
Mon	207	1/7	1443 * 1/7= 206.142857	(207 - 206.142857)²/206.142857 = 0.0036
Tue	222	1/7	1443 * 1/7= 206.142857	(222 - 206.142857)²/206.142857 = 1.2198
Wed	247	1/7	1443 * 1/7= 206.142857	(247 - 206.142857)²/206.142857 = 8.0978
Thu	175	1/7	1443 * 1/7= 206.142857	(175 - 206.142857)²/206.142857 = 4.7049
Fri	205	1/7	1443 * 1/7= 206.142857	(205 - 206.142857)²/206.142857 = 0.0063
Sat	230	1/7	1443 * 1/7= 206.142857	(230 - 206.142857)²/206.142857 = 2.761
Total	1443	1.00	1443	28.5087

Null and alternative hypotheses.

H0​: Police calls occur with the same frequency on the different days of the week.

H1​: At least one day has a different frequency of calls than the other days.

Test statistic:

χ² = ∑ ((O-E)²/E) = 28.509

df = n-1 = 6

p-value = CHISQ.DIST.RT(28.5087, 6) = 0.000

What is the conclusion for this hypothesis​ test?

D. Reject H0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

What is the fundamental error with this​ analysis?

B. Because October has 31​ days, three of the days of the week occur more often than the other days of the week.