Hypothesis Testing and t-distribution in Excel: Statistical Inference - Prof. Douglas L. M, Assignments of Economics

Download Hypothesis Testing and t-distribution in Excel: Statistical Inference - Prof. Douglas L. M and more Assignments Economics in PDF only on Docsity! - 1 - The questions are from the problem set of the Prof. Miller(Fall 2008, ECN 102). The t-distribution in Excel Use the Excel functions TDIST and TINV to answer the following questions. For each question, assume that the sample size or number of observations, n, is equal to 16. (Use n to determine the appropriate number of degrees of freedom.) a. Pr[T >1.6] =TDIST(abs(1.6), 16-1, 1) b. Pr[T < −2.0 or T > 2.0] =TDIST(abs(2.0), 16-1, 2) c. t* such that Pr[T > t *]= 0.05 t* = TINV(0.05*2, 16-1) d. t* such that Pr[T < −t * or T > t *]= 0.05 t* = TINV(0.05, 16-1) Exercise e. t* such that Pr[T > t *]= 0.01 t* = TINV( , ) f. t* such that Pr[T < −.t * or T > t *]= 0.01 t* = TINV( , ) - 2 - Statistical Inference: Hypothesis Tests (For this question, use the data set the data set “A-kids-2007.xls) Question 1. You will analyze the variable "Poverty Status". a. Two-sided test Test the null hypothesis that the population mean poverty rate is 20% (: μ = .20) against the alternative that the population mean is not equal to 20% ( : μ ≠ .20). Perform the test at a significance level of 0.10, use the p-value approach to reach your conclusion. Clearly state and interpret your conclusion. 1  Form  the  hypothesis:  H0:  =  0.2  v.s.  Ha:   0.2 2  Form  the  test  statistic: xbar  0.190711462 s/√n  0.007131169 t‐statistic  ‐1.30252658 3  Calcuate  the  p‐value  for  a  two‐sided  test: degrees  of  freedom  (df)  3035 p‐value  =  TDIST(abs(‐1.3),3035,2)  =  0.192835263 4  Conclusion  and  interpretation Since  p‐nvalue>0.1,  we  fail  to  reject  the  null  hypothesis  of  mu=0.20  at  the  0.1  level  of  significance.  The  data  are  consistent  with  the  true  population  poverty  rate  being  20%.  We  thus  conclude  that  it  is  possible  that  the  true  poverty  rate  is  20%.