atuifel
Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

A study of a local high school tried to determine the mean amount of money that each
student had saved. The study surveyed a random sample of 69 students in the high
school and found a mean savings of 5000 dollars with a standard deviation of 1400
dollars. At the 95% confidence level, find the margin of error for the mean, rounding
to the nearest whole number. (Do not write ).

A Study Of A Local High School Tried To Determine The Mean Amount Of Money That Each Student Had Saved The Study Surveyed A Random Sample Of 69 Students In The class=

Sagot :

Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

  • [tex]\overline{x}[/tex] is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

The margin of error is given by:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.

The standard deviation and sample size are given, respectively, by:

s = 1400, n = 69.

Hence, the margin of error in dollars is given by:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

[tex]M = 1.9955\frac{1400}{\sqrt{69}}[/tex]

M = 336.

More can be learned about the t-distribution at https://brainly.com/question/16162795

#SPJ1

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.