The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272. Do we have evidence to support the claim that young men nationwide have a mean score below 275?
Question
The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272. Do we have evidence to support the claim that young men nationwide have a mean score below 275?
Solution
To answer this question, we would typically conduct a one-sample t-test to compare the sample mean to the population mean. Here are the steps:
-
State the Hypotheses: The null hypothesis would be that the population mean is 275 (H0: μ = 275). The alternative hypothesis would be that the population mean is less than 275 (Ha: μ < 275).
-
Check Assumptions: We assume that the sample is representative of the population and that the scores are normally distributed.
-
Calculate the Test Statistic: The test statistic for a one-sample t-test is calculated as (sample mean - population mean) / (standard deviation / sqrt(sample size)). In this case, we don't have the standard deviation, so we can't calculate the test statistic.
-
Determine the P-value: The P-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis. Without the test statistic, we can't calculate the P-value.
-
Draw a Conclusion: Based on the P-value, we would decide whether to reject the null hypothesis. If the P-value is less than our significance level (typically 0.05), we would reject the null hypothesis and conclude that we have evidence to support the claim that the mean score is less than 275. Without the P-value, we can't draw a conclusion.
In conclusion, without the standard deviation of the sample, we can't conduct a t-test and therefore can't determine whether we have evidence to support the claim that young men nationwide have a mean score below 275.
Similar Questions
For the following scenarios, give the null and alternative hypotheses and state in words what µ represents in your hypotheses.Question 1: The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272. Do we have evidence to support the claim that young men nationwide have a mean score b
On a nationwide test taken by high school students, the mean score was 49 and the standard deviation was 12. The scores were normally distributed. Complete the following statements.(a) Approximately 95% of the students scored between and .(b) Approximately of the students scored between 13 and 85.
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 208 graduating seniors and found the mean score to be 525 with a standard deviation of 115. At the 95% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest tenth.
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 130 graduating seniors and found the mean score to be 458 with a standard deviation of 105. At the 95% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest tenth.
The Director of the Department of Education in Queensland was analysing the last year average mathematics test scores in the schools under his control. He noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, he attempted to determine the factors that account for the differences. Accordingly, he took a random sample of 40 schools across the state and, for each, determined the mean mathematics test score, the percentage of teachers in each school who have at least one university degree in mathematics (math), the mean age, and the mean annual income ($ ‘000) of the mathematics teachers. These data are saved in the t10e5 Excel file.a) Perform a multiple regression analysis on these data with R. What is your sample regression equation?b) Is the model useful in explaining the variation among schools? Explain.c) Are the normality and homoskedasticity conditions satisfied? Explain.d) Is multicollinearity a problem? Explain.e) Interpret and the coefficients. Do you find their signs reasonable? Why or why not? Based on your expectations perform t-tests on the coefficients (use a = 0.05).f) Test the null hypothesis that neither the teachers’ mean age nor their mean annual income has a significant effect on the average mathematics test scores (use a = 0.05).
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.