z Test for a Proportion — Transcript

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1. 0:00hi I'm JD and we're going to be doing
2. 0:03today is a hypothesis test for portion
3. 0:06when we read the problem first it has
4. 0:09been found that forty eight point seven
5. 0:12percent of US households have
6. 0:16investments a random sample of four
7. 0:20hundred heads of households indicated
8. 0:23that 223 have events investments of some
9. 0:27sorts at alpha at the outlet equaling
10. 0:330.02 does this suggests that there is a
11. 0:37difference from what was found before so
12. 0:44if you would pause the video and see if
13. 0:47you can try this one on your own all
14. 0:52right step number one here someone is
15. 0:57you want to list out the hypotheses your
16. 1:01null and your alternative your null
17. 1:05doesn't have equals in it you're sorry
18. 1:09you're no less equals in it your
19. 1:11alternative never has equals in it so
20. 1:14look at your conclusion or what you're
21. 1:16trying to prove does this suggest that
22. 1:19there is a difference well when it says
23. 1:22that is there a difference it doesn't
24. 1:26matter if it's increase or decrease just
25. 1:30that it's one or the other it could be
26. 1:34either/or
27. 1:36so the proportion is not equal to what
28. 1:42was found before is the 48.7% let's
29. 1:46convert that to decimal so it would be
30. 1:48zero point four eight seven and this
31. 1:56would be your claim now your null is
32. 2:02gonna be the opposite so it's going to
33. 2:05be P equals the proportion of the
34. 2:08population equals zero points or eight
35. 2:12seven
36. 2:14step number two is you want to find your
37. 2:17critical values now since it's not equal
38. 2:21to it's going to be a two-tailed test so
39. 2:26it's going to be left
40. 2:30and rights and then this equals half of
41. 2:34the Alpha so this is 0.01 and then this
42. 2:40is 0.01 as well so you need to find
43. 2:44these critical values do that you need
44. 2:48your chart for your z-scores now I need
45. 2:54to find something that's close to this
46. 2:57notice the picture on the bottom has
47. 2:59this so I'm going to look for something
48. 3:02that's close to point nine nine right
49. 3:07because this right here is point zero
50. 3:10one and so the leftovers would be 0.99
51. 3:16you want something close to that which
52. 3:19looks like two point three three is
53. 3:22close to that 233 notice what this is
54. 3:29saying this is the ones and this is the
55. 3:33ones in a tense place in this column and
56. 3:36on top it's a hundreds place so
57. 3:39basically what you do is you see where
58. 3:41the two line up right find your value
59. 3:45first which is 0.99 zero one and look to
60. 3:50see where those line up the row is 2.3
61. 3:56and the column is point zero three okay
62. 3:59so that's hey come up with two point
63. 4:01three three now on this side since this
64. 4:07is a bell-shaped curve and the you know
65. 4:11the you know is normal distribution so
66. 4:14it's symmetrical so this would be zero
67. 4:18and then the other side would be
68. 4:20negative 2.33 right next you want to
69. 4:26calculate your test statistic
70. 4:34now here's the formula Z equals P hat
71. 4:39minus P over the square root of P Q over
72. 4:46N now what's P what's P hat well P hat
73. 4:54is the rapport ssin of your I'm gonna
74. 4:59put all the variables and stuff up here
75. 5:03P hat is the proportion of the sample
76. 5:08which would be 223 over 400 now I'm
77. 5:17going to round this to three decimal
78. 5:19places
79. 5:20so be 223 divided by 400 which is 0.5
80. 5:33ates on my calculator I got zero point
81. 5:36five five seven five now P is the
82. 5:47proportion of success for what we're
83. 5:51looking at which would be the forty
84. 5:54eight point seven percent so that would
85. 5:56be zero points for eight seven Q is 1
86. 6:04minus F it's the proportion of failure
87. 6:11so that would be one minus zero points
88. 6:15for eight seven which is 0.53 and then
89. 6:25my n would be the sample size which here
90. 6:29is 400 all right so I'm just going to
91. 6:33plug all those in so zero points five
92. 6:36five eight minus zero point four eight
93. 6:41seven over the square root of P times Q
94. 6:49zero point four eight seven times zero
95. 6:54point five one three over 400 and before
96. 7:03we move on just to let you know that in
97. 7:06order to use z-scores for a binomial
98. 7:11distribution you have to make sure that
99. 7:14n times P and n times Q are both greater
100. 7:19than five and here it should be obvious
101. 7:22that they are right because I have a
102. 7:26sample of 400
103. 7:31and you know you have such as so anyways
104. 7:36you want to plug this all it's your
105. 7:39calculator and again I'm gonna do two
106. 7:42decimal places just like right here I'm
107. 7:45going to put the whole numerator in
108. 7:48parenthesis so parenthesis
109. 7:51zero points five five eight minus zero
110. 7:55point four eight seven close parenthesis
111. 7:59divided by it's the square root now the
112. 8:03square root acts like a grouping symbols
113. 8:06so just groups all those together so two
114. 8:09square roots and so don't need
115. 8:11parentheses around the denominator so
116. 8:15zero points
117. 8:18for eight seven times zero point five
118. 8:24one three divided by four hundred
119. 8:28clothes for the skirt and they get two
120. 8:34point eight four
121. 8:402.84 falls right there falls in the
122. 8:47rejection region so step number four is
123. 8:52I'm going to reject the null hypothesis
124. 9:00set number five I'm rejecting the null
125. 9:05hypothesis that means I am accepting the
126. 9:08claim so there is enough
127. 9:19evidence
128. 9:23two supports
129. 9:29the claim
130. 9:35that's
131. 9:38there is
132. 9:42a difference
133. 9:52and that's it