Hypothesis Testing Exercises - Revision history

Rb: /* Hypothesis Testing Exercises */

2014-09-16T09:59:53Z

‎Hypothesis Testing Exercises

Rb at 22:23, 15 September 2014

2014-09-15T22:23:37Z

Rb: /* Hypothesis Testing Exercises */

2014-09-15T22:23:13Z

‎Hypothesis Testing Exercises

Rb: /* Hypothesis Testing Exercises */

2014-09-15T21:57:30Z

‎Hypothesis Testing Exercises

Rb: /* Hypothesis Testing Exercises */

2014-09-13T20:36:37Z

‎Hypothesis Testing Exercises

Rb: /* Hypothesis Testing Exercises */

2014-09-13T20:34:27Z

‎Hypothesis Testing Exercises

Rb: /* Hypothesis Testing Exercises */

2014-09-13T20:30:12Z

‎Hypothesis Testing Exercises

Rb: /* Hypothesis Testing Exercises */

2014-09-13T19:49:07Z

‎Hypothesis Testing Exercises

Rb: Created page with " == Hypothesis Testing Exercises ==

Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any he..."

2013-09-22T22:48:11Z

Created page with " == Hypothesis Testing Exercises == <ol> <li>Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any he..."

New page

== Hypothesis Testing Exercises ==

<ol>
<li>Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any health consequences for the population at large. Having some knowledge of statistics, you set up the issue as one of hypothesis testing.
<ol>
<li>What would your null and alternative hypotheses be?</li>
<li>Explain the interpretation of a Type I error and a Type II error in this context.</li>
<li>What sort of costs would arise as a consequence of each type of error?</li>
<li>What sort of sample evidence would be needed to enable a statistical conclusion to be reached?</li>
<li>If suitable sample evidence were available, what advice would you give about the strength of the evidence that would be required to reject your null hypothesis?</li></ol>
</li>
<li>Weekly wages in a particular industry are known to be normally distributed with a '''standard deviation''' of £2.10. An economist claims that the mean weekly income in the industry is £72.40. A random sample of 35 workers yields a mean income of £73.20.
<ol>
<li>What null hypothesis would you specify?</li>
<li>Without any further information, explain the justification for choosing
<ol>
<li>a two tailed alternative hypothesis<math>;</math></li>
<li>an upper one tailed alternative hypothesis.</li></ol>
</li>
<li>Perform the tests for each of these alternative hypotheses in turn, using
<ol>
<li><math>p</math> values</li>
<li>classical hypothesis tests</li>
<li>a suitable confidence interval procedure</li></ol>

at a <math>5\%</math> level of significance.</li></ol>
</li>
<li>This question is a version of Question 2.
Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of <math>15</math> workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the <math>p</math> values required.</li>
<li>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.5</math>,
<ol>
<li>using an upper one sided alternative hypothesis for domestically produced vans<math>;</math></li>
<li>using a two-sided alternative hypothesis for imported vans.</li></ol>
</li></ol>

= Footnotes =

@@ Line 9: / Line 9: @@
 == Hypothesis Testing Exercises ==
-Worked solutions to these questions can be found here: [ Q1], [http://youtu.be/4u7dmz1yD4A?hd=1 Q2 and Q3] and [http://youtu.be/_cPJ_K6Iozk?hd=1 Q4]
+Worked solutions to these questions can be found here: [http://youtu.be/uKIA0Nw9Xig?hd=1 Q1], [http://youtu.be/4u7dmz1yD4A?hd=1 Q2 and Q3] and [http://youtu.be/_cPJ_K6Iozk?hd=1 Q4]
 <ol>

@@ Line 1: / Line 1: @@
@@ Line 7: / Line 9: @@
 == Hypothesis Testing Exercises ==
-Worked solutions to these questions can be found here: [ Q1], [http://youtu.be/4u7dmz1yD4A?hd=1 Q2 and Q3] and [ Q4]
+Worked solutions to these questions can be found here: [ Q1], [http://youtu.be/4u7dmz1yD4A?hd=1 Q2 and Q3] and [http://youtu.be/_cPJ_K6Iozk?hd=1 Q4]
 <ol>
@@ Line 40: / Line 42: @@
 <li><p>using a two-sided alternative hypothesis for imported vans. {<math>t=-5.0632</math>, reject <math>H_0</math>}</p></li></ol>
 </li></ol>
 = Footnotes =
 = Footnotes =

@@ Line 1: / Line 1: @@
@@ Line 4: / Line 6: @@
 == Hypothesis Testing Exercises ==
 <ol>
-<li><p>Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any health consequences for the population at large. Having some knowledge of statistics, you set up the issue as one of hypothesis testing.</p>
+<li><p><math>[L2]</math> Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any health consequences for the population at large. Having some knowledge of statistics, you set up the issue as one of hypothesis testing.</p>
 <ol>
 <li><p>What would your null and alternative hypotheses be?</p></li>
@@ Line 14: / Line 18: @@
 <li><p>If suitable sample evidence were available, what advice would you give about the strength of the evidence that would be required to reject your null hypothesis?</p></li></ol>
 </li>
-<li><p>Weekly wages in a particular industry are known to be normally distributed with a '''standard deviation''' of £2.10. An economist claims that the mean weekly income in the industry is £72.40. A random sample of 35 workers yields a mean income of £73.20.</p>
+<li><p><math>[L2]</math> Weekly wages in a particular industry are known to be normally distributed with a '''standard deviation''' of £2.10. An economist claims that the mean weekly income in the industry is £72.40. A random sample of 35 workers yields a mean income of £73.20.</p>
 <ol>
 <li><p>What null hypothesis would you specify?</p></li>
@@ Line 24: / Line 28: @@
 <li><p>Perform the tests for each of these alternative hypotheses in turn, using</p>
 <ol>
-<li><p><math>p</math> values</p></li>
+<li><p><math>p</math> values {<math>p-val = 0.0244</math> (for two tailed test) and <math>p-val=0.0122</math> (for upper tailed test}</p></li>
 <li><p>classical hypothesis tests</p></li></ol>
 <p>at a <math>5\%</math> level of significance.</p></li></ol>
 </li>
-<li><p>This question is a version of Question 2.</p>
+<li><p><math>[L2]</math> This question is a version of Question 2.</p>
-<p>Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of <math>15</math> workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the <math>p</math> values required.</p></li>
+<p>Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of <math>15</math> workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the <math>p</math> values required. {Do not reject <math>H_0</math> for both, two-tailed and upper tailed test}</p></li>
-<li><p>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.35</math>,</p>
+<li><p><math>[L2]</math> A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.35</math>,</p>
 <ol>
-<li><p>using a lower one sided alternative hypothesis for domestically produced vans<math>;</math></p></li>
+<li><p>using a lower one sided alternative hypothesis for domestically produced vans<math>;</math> {<math>t=-1.5002</math>, do not reject <math>H_0</math>}</p></li>
-<li><p>using a two-sided alternative hypothesis for imported vans.</p></li></ol>
+<li><p>using a two-sided alternative hypothesis for imported vans. {<math>t=-5.0632</math>, reject <math>H_0</math>}</p></li></ol>
 </li></ol>
 = Footnotes =

@@ Line 31: / Line 31: @@
 <li><p>This question is a version of Question 2.</p>
 <p>Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of <math>15</math> workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the <math>p</math> values required.</p></li>
-<li><p>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.4</math>,</p>
+<li><p>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.35</math>,</p>
 <ol>
 <li><p>using a lower one sided alternative hypothesis for domestically produced vans<math>;</math></p></li>

@@ Line 31: / Line 31: @@
 <li><p>This question is a version of Question 2.</p>
 <p>Weekly wages in a particular industry are known to be normally distributed, with an unknown variance. An economist claims that the mean weekly income in the industry is £72.40. A random sample of <math>15</math> workers gives a sample mean of £73.20 and a sample standard deviation of £2.50. Redo part (3) of Question 2 with this new information. You will need to use EXCEL to compute the <math>p</math> values required.</p></li>
-<li><p>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.5</math>,</p>
+<li><p>A motoring organisation is examining the reliability of imported and domestically produced vans. Service histories for <math>500</math> domestically made and <math>500</math> imported vans were examined. Of these, <math>159</math> domestically produced vans and <math>121</math> imported vans had repairs for breakdowns. Test the hypothesis that the true proportion of breakdowns to be expected in the two populations of vans is <math>0.4</math>,</p>
 <ol>
 <li><p>using a lower one sided alternative hypothesis for domestically produced vans<math>;</math></p></li>

Hypothesis Testing Exercises - Revision history

Rb: /* Hypothesis Testing Exercises */

Rb at 22:23, 15 September 2014

Rb: /* Hypothesis Testing Exercises */

Rb: /* Hypothesis Testing Exercises */

Rb: /* Hypothesis Testing Exercises */

Rb: /* Hypothesis Testing Exercises */

Rb: /* Hypothesis Testing Exercises */

Rb: /* Hypothesis Testing Exercises */

Rb: Created page with " == Hypothesis Testing Exercises == Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any he..."

Rb: Created page with " == Hypothesis Testing Exercises ==

Imagine that you are a member of a team of scientific advisors considering whether genetic modification of crops has any he..."