Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately ² = 47.1. However, a random sample of 13 colleges and universities in Kansas showed that x has a sample variances² = 84.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1.(a) What is the level of significance?State the null and alternate hypotheses.O Ho: 0² = 47.1; H₂₁:0² < 47.1O Ho: 0² = 47.11 H₁: 0² > 47.1O Ho: 0² < 47.1; H₂:0² = 47.1O Ho: 0² = 47.1; H₂:0² 47.1(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)What are the degrees of freedom?What assumptions are you making about the original distribution?O We assume a uniform population distribution.O We assume a normal population distribution.O We assume a exponential population distribution.O We assume a binomial population distribution.(c) Find or estimate the P-value of the sample test statistic.OP-value > 0.100O 0.050 < P-value < 0.100O 0.025 < P-value < 0.050O 0.010 < P-value < 0.025O 0.005 < P-value < 0.010O P-value < 0.005(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?O Since the P-value > a, we fail to reject the null hypothesis.O Since the P-value > a, we reject the null hypothesis.O Since the P-value sa, we reject the null hypothesis.O Since the P-values a, we fail to reject the null hypothesis.(e) Interpret your conclusion in the context of the application.O At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.O At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas.

It is given that Sample size n = 13 Sample variance s2 = 84.2 Level of significance = 5% Note :…

Letx represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately 247.1. Howeves a random sample of 13 colleges and universities in Kansas showed that has a sample varian s² = 84.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. (a) What is the level of significance? State the null and alternate hypotheses. Hol 0² 47.11 M₂ ²47.1 Hol 0² 47.11 M₁ 0² > 47.1 OHội gì ca đi Hồi gần 4 ⒸHg: 0² 47.11 H₂:0² 47.1 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a uniform population distribution. Ⓒ We assume a normal population distribution. We assume a exponential population distribution. O We assume a binomial population distribution. (c) Find or estimate the P-value of the sample test statistic. OP-value> 0.100 O 0.050 < P-value < 0.100 O 0.025 P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 P-value < 0.010 OP-value < 0.005

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS