Question

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 126 students who averaged 34.8 texts per day. The standard deviation was 18.7 texts. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a ? v distribution and texts. b. With 98% confidence the population mean number of texts per day is between c. If many groups of 126 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. License Points possible: 1 This is attempt 1 of 1.

Answer 1

Answer:-

Given that:-

(a) t-distribution

here t-distribution should be used as the population standard deviation$(\sigma)$ is not given

(b)

Given

n=126 s=18.7

X = 34.8

98% confidence interval for POPulation Mean is

$(\overline{X}-t*\frac{s}{\sqrt{n}}<\mu<\overline{X}+t*\frac{s}{\sqrt{n}})$

ME=margin of error

$ME=t*\frac{s}{\sqrt{n}}$

t=critical value

$\alpha =1-0.98=0.02$

$Z_{critical}=Z_{0.02/2}=2.3658$

$ME=2.3658*\frac{18.7}{\sqrt{126}}$

$ME=3.95$

Now, 98% Confidence interval for Population Mean is

$\overline{x}\pm Z_{critical}\times \frac{s}{\sqrt{n}}$

$=34.8\pm 2.3658\times \frac{18.7}{\sqrt{126}}$

$=34.8\pm 3.95$

$=30.85,38.75$

98% confidence interval for population mean is $(34.8-3.95<\mu<34.8+3.95)$

$(30.85 <\mu< 38.75)$ is the 98% confidence interval for population mean

#98% confidence interval for population mean number of text per day is between 30.85 and 38.75

c) If many groups of 126 randomly selected days were observed, then a different confidence interval would be produced from each group. About 98 percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives and about 2 percent will not contain the true population mean number of hours of sunlight that the solar panel receives