Question #1 (17 points) A study indicated that individuals filing their income t
ID: 1112099 • Letter: Q
Question
Question #1 (17 points) A study indicated that individuals filing their income tax returns early received an average refund of $1,156. The researcher contends that a reason individuals file their tax returns late (file between April 10 to April 15) is that, on average, these individuals receive lower refunds than do early filers. For a sample of 320 "late income-tax filers," the sample mean refund was $925 (a) Assuming that the population standard deviation of late income-tax filers' returns is $1,450, test the hypothesis to support or reject the researcher's contention. Clearly show your hypothesis testing steps (state your null and alternative hypotheses, indicate your level of significance, test statistic, etc.) and manual (hand and calculator) calculations in 4 decimal places, where possible (b) What is the relevance of hypothesis testing in business and economics?Explanation / Answer
a) We will check for the null hypothresis.
H0: refunds= 1156
against
Ha: refunds < 1156
We will calculate the z-value =( X(bar)-µ)/std. deviation
t = (925-1156)/1450 =-0.16 The z- calculated is sufficiently large( left- tail test) we do not reject the null hypothesis at 5% level of significance.
b) The hypothesis testing help us in making the decision given the sample information