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Complete Question
A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 210 students who averaged 28 texts per day. The standard deviation was 21 texts.
Round your answers to two decimal places.
A. The sampling distribution follows a [ Select ] ["F", "normal", "T", "Chi-square"] distribution.
B. With 95% confidence the population mean number of texts per day of is between [ Select ] ["24.92", "25.79", "27.37", "25.14"] and [ Select ] ["31.19", "31.20", "29.28", "30.86"] texts.
C. If many groups of 210 randomly selected students are studied, then a different confidence interval would be produced from each group. About [ Select ] ["5", "95", "1", "99"] percent of these confidence intervals will contain the true population mean number of texts per day and about [ Select ] ["95", "99", "5", "1"] percent will not contain the true population mean number of texts per day.
Answer:
a. With 95% confidence the population mean number of texts per day is between and
texts.
b
If many groups of 132 randomly selected members are studied, then a different confidence interval would be produced from each group. About <u>95%</u> percent of these confidence intervals will contain the true population number of texts per day and about <u>5%</u> percent will not contain the true population mean number of texts per day.
Step-by-step explanation:
From the question we are told that
The sample size is
The population mean is
The standard deviation is
Generally the standard error of mean is mathematically evaluated as
substituting values
Given that the level of confidence is 95% then the level of significance will be
5%
=>
Now the critical values of this level of significance is obtained from the critical value table as
Generally the 95% confidence interval is mathematically represented as
substituting values
and
So the interval is