He/She/Them ~ According to a recent article from the Pew Research Center, “On the Cusp of Adulthood and Facing an Uncertain Future: What We Know About Gen Z So Far”: “Ideas about gender identity are rapidly changing in the U.S., and Gen Z is at the front end of those changes. Gen Zers are much more likely than those in older generations to say they personally know someone who prefers to go by gender-neutral pronouns, with 35% saying so.” Gen Z refers to individuals between 1997 and 2012. A group of students in an introductory statistics class wants to know what proportion of students at their university say they personally know someone who prefers to go by gender-neutral pronouns. They survey a random sample of 200 students and find that 68 say they personally know someone who prefers to go by gender-neutral pronouns. 1. Using the information from the university student sample, construct a 95% confidence interval for the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns. ( , ) 2. Which of the following conditions must be met for the confidence interval to be valid? Select all that apply.A. The value for p must be less than 0.10 to provide evidence against the null hypothesis. B. The observations must be independent of one another. C. The sample proportion must be normally distributed. D. There must be at least 10 'success' and 10 'failure' observations in the sample. 3. The information from the survey gives a standard error of ???̂=SEp^= 0.0335. Which of the statements below is a correct interpretation of the standard error? A. The sample proportion is different from the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns approximately 3.35% of the time.B. We have strong evidence that the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns is contained in a confidence interval.C. On average, for repeated samples of this size, we expect the sample proportion to be approximately 0.0335 from the true population proportion.D. We can be 3.35% confident that our sample proportion is correctly calculated. 4. If the statistics students want to estimate the true proportion of Gen Zers who say they personally know someone who prefers to go by gender-neutral pronouns with 95% confidence and a margin of error of no more than 1.1%, what size sample should they take? Use the value from the Pew Research Center report as a planning value for ?∗p∗, that is, ?∗=0.35p∗=0.35. Round your ?∗z∗ value to exactly 3 decimal places. ?=n= 5. A student group at a different university surveys 345 students at their university and calculate a 95% confidence interval for the proportion of students at their university who say they personally know someone who prefers to go by gender-neutral pronouns to be (0.314, 0.4). Which of the following statements are appropriate interpretations in this scenario? Select all that apply.A. We can be 95% confident that, on average, the margin of error will vary no more than the size of the standard error. B. We can be 95% confident that the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns to be contained in the interval (0.314, 0.4). C. On average, 95% of the time we can expect any sample proportion from a sample of 345 students at the university who say they personally know someone who prefers to go by gender-neutral pronouns to be in the interval (0.314, 0.4). D. If the statistics students collected 100 samples of size n = 345 from this population and constructed 100 new 95% confidence intervals, they could expect approximately 95 of them to contain the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns. 6. If, instead, these students (from question #5) calculate a 99% confidence interval for the true proportion of students at their university who say they personally know someone who prefers to go by gender-neutral pronouns, this new interval would be the 95% confidence interval.

Question

He/She/Them ~ According to a recent article from the Pew Research Center, “On the Cusp of Adulthood and Facing an Uncertain Future: What We Know About Gen Z So Far”: “Ideas about gender identity are rapidly changing in the U.S., and Gen Z is at the front end of those changes. Gen Zers are much more likely than those in older generations to say they personally know someone who prefers to go by gender-neutral pronouns, with 35% saying so.” Gen Z refers to individuals between 1997 and 2012. A group of students in an introductory statistics class wants to know what proportion of students at their university say they personally know someone who prefers to go by gender-neutral pronouns. They survey a random sample of 200 students and find that 68 say they personally know someone who prefers to go by gender-neutral pronouns. 1. Using the information from the university student sample, construct a 95% confidence interval for the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns. ( , ) 2. Which of the following conditions must be met for the confidence interval to be valid? Select all that apply.A. The value for p must be less than 0.10 to provide evidence against the null hypothesis. B. The observations must be independent of one another. C. The sample proportion must be normally distributed. D. There must be at least 10 'success' and 10 'failure' observations in the sample.  3. The information from the survey gives a standard error of ???̂=SEp^= 0.0335. Which of the statements below is a correct interpretation of the standard error? A. The sample proportion is different from the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns approximately 3.35% of the time.B. We have strong evidence that the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns is contained in a confidence interval.C. On average, for repeated samples of this size, we expect the sample proportion to be approximately 0.0335 from the true population proportion.D. We can be 3.35% confident that our sample proportion is correctly calculated. 4. If the statistics students want to estimate the true proportion of Gen Zers who say they personally know someone who prefers to go by gender-neutral pronouns with 95% confidence and a margin of error of no more than 1.1%, what size sample should they take? Use the value from the Pew Research Center report as a planning value for ?∗p∗, that is, ?∗=0.35p∗=0.35. Round your ?∗z∗ value to exactly 3 decimal places.  ?=n=   5. A student group at a different university surveys 345 students at their university and calculate a 95% confidence interval for the proportion of students at their university who say they personally know someone who prefers to go by gender-neutral pronouns to be (0.314, 0.4). Which of the following statements are appropriate interpretations in this scenario? Select all that apply.A. We can be 95% confident that, on average, the margin of error will vary no more than the size of the standard error. B. We can be 95% confident that the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns to be contained in the interval (0.314, 0.4). C. On average, 95% of the time we can expect any sample proportion from a sample of 345 students at the university who say they personally know someone who prefers to go by gender-neutral pronouns to be in the interval (0.314, 0.4). D. If the statistics students collected 100 samples of size n = 345 from this population and constructed 100 new 95% confidence intervals, they could expect approximately 95 of them to contain the true proportion of students at the university who say they personally know someone who prefers to go by gender-neutral pronouns.  6. If, instead, these students (from question #5) calculate a 99% confidence interval for the true proportion of students at their university who say they personally know someone who prefers to go by gender-neutral pronouns, this new interval would be       the 95% confidence interval.

Accepted Answer

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