rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia.7287169314227164541606073273317144107491441842245911652415542241143324197426631103934715239801521491249610(i) Find the median. (Use 1 decimal place.)(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance.(b) Find the number of runs R, n1, and n2. Let n1 = number of values above the median and n2 = number of values below the median.R n1 n2 (c) In the case, n1 > 20, we cannot use Table 10 of Appendix II to find the critical values. Whenever either n1 or n2 exceeds 20, the number of runs R has a distribution that is approximately normal, as follows. We convert the number of runs R to a z value, and then use the normal distribution to find the critical values. Convert the sample test statistic R to z using the following formula. (Use 2 decimal places.)z =R – μRσR(d) The critical values of a normal distribution for a two-tailed test with level of significance α = 0.05 are -1.96 and 1.96 (see Table 5(c) of Appendix II). Reject H0 if the sample test statistic z ≤ -1.96 or if the sample test statistic z ≥ 1.96. Otherwise, do not reject H0.Sample z ≤ -1.96-1.96 < sample z < 1.96Sample z ≥ 1.96Reject H0Fail to reject H0Reject H0

(a). Compute the value of median for the given data: The data represents the rain amounts (X) for…

Answered: rofessor Cornish studied rainfall…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 38HP

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rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia.

7	28	7	1	69	3	1	4	22	7	16	4	54	160
60	73	27	3	3	1	7	144	107	4	91	44	1	8
4	22	4	59	116	52	4	155	42	24	11	43	3	24
19	74	26	63	110	39	34	71	52	39	8	0	15	2
14	9	1	2	4	9	6	10

(i) Find the median. (Use 1 decimal place.)

(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance.

(b) Find the number of runs R, n₁, and n₂. Let n₁ = number of values above the median and n₂ = number of values below the median.

R
n₁
n₂

(c) In the case, n₁ > 20, we cannot use Table 10 of Appendix II to find the critical values. Whenever either n₁ or n₂ exceeds 20, the number of runs R has a distribution that is approximately normal, as follows.

We convert the number of runs R to a z value, and then use the normal distribution to find the critical values. Convert the sample test statistic R to z using the following formula. (Use 2 decimal places.)

z =

R – μ_R

σ_R

(d) The critical values of a normal distribution for a two-tailed test with level of significance α = 0.05 are -1.96 and 1.96 (see Table 5(c) of Appendix II). Reject H₀ if the sample test statistic z ≤ -1.96 or if the sample test statistic z ≥ 1.96. Otherwise, do not reject H₀.

Sample z ≤ -1.96	-1.96 < sample z < 1.96	Sample z ≥ 1.96
Reject H₀	Fail to reject H₀	Reject H₀

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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7	28	7	1	69	3	1	4	22	7	16	4	54	160
60	73	27	3	3	1	7	144	107	4	91	44	1	8
4	22	4	59	116	52	4	155	42	24	11	43	3	24
19	74	26	63	110	39	34	71	52	39	8	0	15	2
14	9	1	2	4	9	6	10

7	28	7	1	69	3	1	4	22	7	16	4	54	160
60	73	27	3	3	1	7	144	107	4	91	44	1	8
4	22	4	59	116	52	4	155	42	24	11	43	3	24
19	74	26	63	110	39	34	71	52	39	8	0	15	2
14	9	1	2	4	9	6	10

7	28	7	1	69	3	1	4	22	7	16	4	54	160
60	73	27	3	3	1	7	144	107	4	91	44	1	8
4	22	4	59	116	52	4	155	42	24	11	43	3	24
19	74	26	63	110	39	34	71	52	39	8	0	15	2
14	9	1	2	4	9	6	10