A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 96 students in the high school and found a mean of 165 messages sent per day with a standard deviation of 52 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number.
Question
A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 96 students in the high school and found a mean of 165 messages sent per day with a standard deviation of 52 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number.
Solution
To find the margin of error for the mean at the 95% confidence level, we first need to find the standard error. The standard error (SE) is calculated by dividing the standard deviation (SD) by the square root of the sample size (n).
In this case, the standard deviation is 52 messages and the sample size is 96 students.
SE = SD / sqrt(n) SE = 52 / sqrt(96) SE = 52 / 9.8 SE = 5.31
Next, we need to find the critical value for a 95% confidence level. The critical value for a 95% confidence level in a normal distribution is approximately 1.96.
Finally, we calculate the margin of error by multiplying the standard error by the critical value.
Margin of Error = SE * Critical Value Margin of Error = 5.31 * 1.96 Margin of Error = 10.41
Rounding to the nearest whole number, the margin of error for the mean is 10 messages.
Similar Questions
Calculate the margin of error and construct the confidence interval for the population mean using the Student's t-distribution (you may assume the population data is normally distributed).10:41 p.m.x̄ =36.4, n=43, s=17, 98% confidence
At a middle school campus, the number of text messages sent by males and females were analyzed. Twelve random female students and 12 random male students were asked how many text messages they sent that day. The following data was calculated from the number of text messages sent during the day for males and females. Females MalesMean 112 99Median 68 52Mode 78 78Range 84 76Based on these samples, what generalization can be made? A. A female sent the most number of text messages out of both groups. B. Not enough information is provided to draw any of these conclusions. C. Males sent more total text messages than females. D. The modes of text messages sent by both males and females are the same.
A survey of a random sample of 1,500 young Americans found that 87% had earned their high school diploma. Based on these results, the 95% confidence interval for the proportion of young Americans who have earned their high school diploma is (0.853,0.887) What is the margin of error for this confidence interval? 0.87 0.017 0.95 0.034
Researchers surveyed 1,150 high school students in CA to estimate the proportion of all high school students who vape. 368 of the surveyed students said they do vape. What is the margin of error of the 95% confidence interval?
In a recent survey of 800 teens with drivers licences, 372 said they text while driving. Develop a 90% confidence interval for the proportion of teens who actually text while driving.As always, step one is understand what the question is asking us to do. What are you expected to do with this question?
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.