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current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. Ho: 0²5.1: M₂: ²8.1 Mgl 0²-5.31 M₂:0² > 5.1 Mo: 0²5.11 M₁: 0²-5.1 Ho: 0²5.11 M₂: ²5.1 (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 normal population distribution. We assume a binomial population distribution. We assume a exponential population distribution. We assume a uniform 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 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 OP-value < 0.005

current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. Ho: 0²5.1: M₂: ²8.1 Mgl 0²-5.31 M₂:0² > 5.1 Mo: 0²5.11 M₁: 0²-5.1 Ho: 0²5.11 M₂: ²5.1 (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 normal population distribution. We assume a binomial population distribution. We assume a exponential population distribution. We assume a uniform 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 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 OP-value < 0.005

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately 2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 3.1. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: 0² = 5.1; H₁: 0² # 5.1 O Ho: 0² = 5.1: H₁: 0² > 5.1 O Ho: 0² < 5.1; H₂:0² = 5.1 O Ho: 0² = 5.1; H₁:0² < 5.1 (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 normal population distribution. O We assume a binomial population distribution. O We assume a exponential population distribution. O We assume a uniform 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 (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 ≤ a, we reject the null hypothesis. O Since the P-value ≤ 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 that the variance of age at first marriage is less than 5.1. O At the 5% level of significance, there is sufficient evidence to conclude that the variance of age at first marriage is less than 5.1.
Transcribed Image Text:Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately 2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 3.1. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: 0² = 5.1; H₁: 0² # 5.1 O Ho: 0² = 5.1: H₁: 0² > 5.1 O Ho: 0² < 5.1; H₂:0² = 5.1 O Ho: 0² = 5.1; H₁:0² < 5.1 (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 normal population distribution. O We assume a binomial population distribution. O We assume a exponential population distribution. O We assume a uniform 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 (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 ≤ a, we reject the null hypothesis. O Since the P-value ≤ 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 that the variance of age at first marriage is less than 5.1. O At the 5% level of significance, there is sufficient evidence to conclude that the variance of age at first marriage is less than 5.1.
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