Week 2 One-Sample Hypothesis Team Paper (Wages)
Week 2 One-Sample Hypothesis Team Paper (Wages)
CSU - Dominguez hills
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Date Created: 11/15/15
One Sample 1 One Sample Hypothesis Testing Paper Names Week 2 Team Assignment One Sample 2 One Sample Hypothesis Testing Paper Since the economy began a decrease back in 2007 the United States Government has struggled with developing different programs to stimulant the economy and creating more employment opportunities The programs included Cash for Clunkers and the Home Buyers Tax Credit However even with the implementation of such programs unemployment rates still rose hitting as high as 97 percent in October 2009 The research performed for this assignment is determining whether or not there was a significant decrease in the workforce over a 4 month period The workforce in the world is decreasing quite rapidly as people are losing their jobs every day In this research we are testing to see if the employment rate of a random group of people has had a decrease in employment workforce or increase in employment We have a small sample from which we see who is employed and who is not employed regardless of gender and ethnicity Since our sample size is small we will be conducting a student s t test The hypotheses for our test are H 39u d H The mean number of unemployed is less than 14 14H 39u E 1 The mean number of unemployed is greater than or equal to 14 Where there are 14 people unemployed and our team will use our sample to decide if we should reject the null hypothesis or accept it using a 5 step hypothesis test Steps in Hypothesis Testing 1 Identify the null hypothesis HO and the alternate hypothesis Ha 2 Choose a The value should be small usually less than 10 It is important to consider One Sample 3 One Sample Hypothesis Testing Paper the consequences of both types of errors 3 Select the test statistic and determine its value from the sample data This value is called the observed value of the test statistic Remember that a t statistic is appropriate for a small number of samples 4 Compare the observed value of the statistic to the critical value obtained for the chosen a 5 Make a decision If the test statistic falls in the critical region If the test statistic does not fall in the critical region Reject H0 in favor of Ha Conclude that there is not enough evidence to reject HO Small samples Paired t test When the sample size is less than 30 and we are relying on the sample standard deviation the test statistic is the t statistic calculated as follows a the populations are normally distributed b the populations are independent c the standard deviations of the sampled populations are equal Given that we are using a sample to draw conclusions about a population it is entirely likely that there is little knowledge One Sample 4 One Sample Hypothesis Testing Paper of the nature of the population For that reason to assure equal standard deviations szp a pooled value is used The pooled value comes from a formula that in effect provides an average value for the variance of each population E W ll ii 39 KHz 135 111 r12 E Example X1 81 HI X2 Sz 42 n2 If 11 135213 in 4315 Step3 15 139213 142215 13 111 112 E E1 7 r 1 1 r 1 2 ill 5 1 s 1a33 1 146 126 1633115 113 2 1531 1306 step 4 you now have to select a critical value using the nl rule for a t test In the case of 2 small samples obtain the 11 value by using this easy equation 11 n1 n2 2 in the example that gives 1513 2 26 Go to the Student s t table and use the n n 1 n2 2 for degrees of freedom to look up the critical value in the field depending on the alpha and the choice of a 1 or 2 tail test Alpha 005 tc t1645 gt teak 1306 Do not reject Null Hypothesis Based on the tests performed above there is no significant evidence to reject HO One Sample 5 One Sample Hypothesis Testing Paper The null hypothesis relies on one or more sample means where research was performed in order to draw a conclusion about the value of the population tested for the subject A failure to reject H0 will provide the research with a null result In other words research performed has provided a nonsignificant result We can almost determine that we will fail to reject the null hypothesis when H0 is true However if H0 is false we may fail to reject H0 because there is no significant power in the results presented The conclusion would be to fail to reject the null hypothesis in both instances Based on the tests performed above it has been concluded that there is not enough information to determine whether or not there was a significant change in the workforce unemployment over the last four months The information used includes normal distribution of a small independent population The team is not rejecting the null hypothesis because our research observes a sample that does not agree with the null hypothesis and does not provide the amount of information feasible to allow us to decide it is false or the alternate hypothesis true The study shows that the null is questionable and we cannot determine the null is true To answer the question determining whether or not there was a significant decrease in the workforce over a 4 month period the team would have to expand upon the sample that was researched In this case a four month period was not a long enough period of time to determine if there was an increase or decrease in unemployment A better determination may be made if the team were to perform research over a five year period The larger the sample in this case would show stronger results perhaps of an increase and a decrease If a sample size larger than 30 was used to performer a second sample test the team would then be able to use a Z test which may provide a more accurate result
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