A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 104 students who averaged 32.7 texts per day. The standard deviation was 19.8 texts.Round answers to 3 decimal places where possible.a. To compute the confidence interval use a ? t z  distribution.b. With 98% confidence the population mean number of texts per day is between  and   texts.c. If many groups of 104 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.

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Asked Oct 19, 2019
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A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 104 students who averaged 32.7 texts per day. The standard deviation was 19.8 texts.Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 98% confidence the population mean number of texts per day is between  and   texts.

c. If many groups of 104 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day. 

 

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Expert Answer

Step 1

Assume the standard deviation is given for Sample 104 students.

The provided information is:

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Sample Mean(X32.7 Samlpe standard deviation (s) =19.8 Sample size(n) 104

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Step 2

a)

To use t distribution, there must behold following conditions.

  • the population standard deviation is unknown.
  • The data should follow normal distribution.

Here, the population standard deviation is unknow...

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(0.01,df-1-1-103 )S CI Xt 2.6244x19.8 =32.7t v104 =32.7 5.095 =(27.605, 37.795) Thus, the 98% confidence the population mean number of texts per day lies between 27.605 to 37.795

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