a. State the researcher’s null and alternative hypothesis.b. At α = 0.01, test your hypothesis. Show all your calculations to receive full credit. 1. Individuals filing federal income tax returns prior to March 31received an average refund of $1080. Consider the population of lastminute filers who mail their tax return "late" in April. A researchersuggests that a reason individuals wait until the last minute is that onaverage these individuals receive lower refunds than do early filers.For a sample of 400 individuals who filed a tax return in April, thesample mean refund was $950. Based on prior experience apopulation standard deviation of o = $1500 may be assumed. (5 pointseach – total 15 points)a. State the researcher's null and alternative hypothesis.b. At a = 0.01, test your hypothesis. Show all your calculations toreceive full credit.

Name: a. State the researcher’s null and alternative hypothesis.b. At α = 0.
Uploaded: 2024-03-20T07:07:12.000Z
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Description: a. State the researcher’s null and alternative hypothesis.b. At α = 0.01, test your hypothesis. Show all your calculations to receive full credit. 1. Individuals filing federal income tax returns prior to March 31received an average refund of $1080.

Given Information: Hypothesized value μ0=$1080 Sample size (n) = 400 Sample mean (x¯) = 950 Population standard deviation (σ) = 1500 Significance level α = 0.01 State the Hypothesis as follows: Null Hypothesis: H0:μ=1080 Alternative Hypothesis: H1:μ<1080 Since, population standard deviation is known and sample size is large enough (>30), we use z-testTest statistic is given by the formula: Z=x¯-μ0σn Substitute the given values: Z=950-10801500400=-13075=-1.7333 Thus, the value of the test statistic is -1.7333 Using a standard normal table, for a left tailed test critical value at 0.01 significance level is: -2.3263 Since, the computed value of the test statistic is greater than the critical value, we fail to reject the null hypothesis. There is insufficient evidence to conclude that on average these individuals receive lower refunds than do early filers.