HOMEWORK #5HOMEWORK #5Hypothesis TestingDirections: Answer the following questions using the information given in the following paragraph. Usingdata from the 2020 Decennial Census you find...

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HOMEWORK #5 HOMEWORK #5 Hypothesis Testing Directions: Answer the following questions using the information given in the following paragraph. Using data from the 2020 Decennial Census you find that the average age of the US population in 2020 was 42 years old (µX = 42). Suppose that you want to test whether the average age of a sample of 2020 GSS respondents (N = 900 valid cases) has a different mean age from the entire US population. Imagine that you calculated the average age of the GSS sample to be 46 years old (X = 45.51)with a sample standard deviation of 13.09 years (SX = 13.09). 1. Conduct a hypothesis test to determine whether the average age of the GSS sample is different from the entire US population (as described by Census data). Use a 0.05 level of significance. Interpret your results. (You must use the five steps for Hypotheses Testing). 1 Directions: The Institute for gender Equality in Education is interested in knowing if a gender disparity in education exists in the United States. Suppose that U.S. Census data showed that, nationally, the population of adult (age 18 +) Americans had a mean education of 13.62 years (µX = 13.62) in the year 2020. Imagine that sample data for non-institutionalized English-speaking adult women from the 2020 General Social Survey revealed that a random sample of 62 respondents had a mean education of 14.81 years (X = 14.81) with a sample standard deviation of 1.2 (SX = 1.2). 2. Conduct a hypothesis test to determine whether the true population mean education for women is greater than the national population mean for men. Use a 0.05 level of significance. Interpret your results. (You must use the five steps for Hypotheses Testing). 2 Directions: Suppose that U.S. Census data showed that, nationally, the American adult(age 18 +) pop- ulation had , on average, 1.86 children (µX = 1.86) in the year 2020. Imagine that sample data for non- institutionalized English-speaking “Very religious” adults from the 2020 General Social Survey revealed that a random sample of 62 very religious respondents had a mean number of children of 14.81 years (X = 14.81) with a sample standard deviation of 1.2 (SX = 1.2). 3. Conduct a hypothesis test to determine whether the true population mean number of children for very religious individuals is greater than then the national population average.Use a 0.05 level of significance. Interpret your results.(You must use the five steps for Hypotheses Testing). 3