Home> Questions>Q 5952
Next
In Process

AcedStudy Latest Questions

PbCstlo
  • 0
Tyro
Asked: 2021-04-07T09:48:32+00:00 In: ,

Problem Solving

  • 0

Miss Romero noted that the mean scores of a random sample of 15 Grade 8 students who had taken a special test was 80.5. If the standard deviation of the scores was 3.1, and the sample came from an approximately normal population, find the point and the interval estimates of the population mean, using 95% confidence.

question

You must login to add an answer.

Need An Account,

1 Answer

  2. acedstud
    This answer was edited.

    The point estimate for the population mean, \mu, is the sample mean, \bar{x}. So, given that the mean score of a random sample of 15 Grade 8 students who had taken a special test was 80.5, that is, \bar{x}=80.5.

    Thus, the point estimate is 80.5.

     

    The interval estimate for the population mean, \mu, is given by \bar{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}, where \bar{x} is the sample mean, \sigma is the population standard deviation, and n is the sample size.

    So, given that the mean score of a random sample of 15 Grade 8 students who had taken a special test was 80.5, the standard deviation is 3.1 and the sample size is 15. For 95% confidence interval, z_{\alpha/2}=1.96.

    Thus, the interval estimate is 80.5\pm1.96\times\dfrac{3.1}{\sqrt{15}}=80.5\pm1.57=(78.93, 82.07).

Related Questions