Chapter 9, Problem 1CS

To determine

To find: The conclusion from the given data.

Answer to Problem 1CS

The conclusion from the given data is the high record occurred more recently than the low record which means $P>0.5$ .

Explanation of Solution

Given information:

The probability is $p$ , $H_0:p=0.5$ and $H_1:p>0.5$ . The given data is shown in table below.

Date	High	Year	Low	Year	More Recent
Jan 1	69	2005	-14	1881	High
8	73	2008	0	1878	High
15	77	1932	4	1886	High
22	76	1927	I	1893	High
29	76	1975	2	1873	High
Feb 5	70	1 99l*	-2	1918*	High
12	74	1999	4	1899	High
19	74	1939	4	1903	High
26	74	1 932	12	1970	Low
Mar 5	83	1976	6	1872	High
12	89	1990	11	1900	High
19	87	1645	12	1876	High
26	87	1921	23	1955	Low
Apr 2	89	1963	23	1907	High
9	90	1 959	28	1972*	Low
16	92	2002	29	1928	High
23	95	1960	33	1933*	High
30	92	1642	34	1874	High
May7	95	1930	38	1970	Low
14	93	1956	41	1928	High
21	95	1934	41	1907	High
28	97	1941	42	1961	Low
Jun 4	99	1925	46	1929*	Low
11	101	1 91 1	45	1913	Low
18	97	1944	51	1965.	Low
25	100	1997	53	1902	High
Ju l 2	I OI	1 898	55	1 940	Low
9	104	1936	55	1891	High
16	104	1988	56	1930*	High
23	102	201 1	56	1 890	High
30	99	1953	56	1914	High
Aug 6	106	1918	53	1912	High
13	101	1 881	55	1 930*	Low
20	101	1983	50	1896	High
27	100	1987	51	1885	High
Sep 3	98	1953	48	1909*	High
10	98	1983	44	1883	High
17	96	1991	44	1923	High
24	99	2010	39	1963	High
Oct 1	93	1941*	36	1899	High
8	91	2007	36	1964*	High
15	87	1975	32	1874	High
22	84	1979*	29	1895	High
29	82	191&	30	1976*	Low
Nov 5	81	2003*	20	1879	High
12	77	1912*	24	1926	Low
19	77	1928	18	1891	High
26	74	1979	17	1950	High
Dec 3	71	2012	15	1976	High
10	67	1966*	4	1876	High
17	64	1984*	10	1876	High
24	69	1933	5	1983	Low

Concept used:

MINITAB is used.

Calculation:

The MINITAB output is shown below.

  

Figure-1

From Figure-1, the $p$ value is $0$ .

From significance level, $\alpha =0.05$ and $\alpha =0.01$ .

Since, the $p$ value is less than the value of $\alpha$ .

Thus, null hypothesis is rejected.

Therefore, the conclusion from the given data is the high record occurred more recently than the low record which means $P>0.5$ .