having trouble with number 6 and 7 05934 B 00934 C 04066 D 0

having trouble with number 6 and 7

)0.5934 B) 0.0934 C) 0.4066 D) 0.9066 6) Construct a 95% confidence interval for the population mean, Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual eanings of $3 standard deviation of $677. Bretly iaterpret Your Ainer ean annual earnings of $3120 with a D) (52657, $2891) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. A) ($2135, $2567) B) ($2803, $3437) C) ($1324, $1567) 7) When 300 community college students were surveyed, 145 said they have a passport Construct a 95% confidence interval for the proportion of community college students that have a passport. Write a brief interpretation. 3402 2.036202.887 2 878 3

Solution

6. Sample Mean = $ 3120

our confidence interval is = 95%

=> df = (total number of workers - 1) = 20-1 = 19

now we\'ll use the t table and select the colume with the confidence interval of 95% and go down the colume and select the element where df is = 19

=> the t value is = 2.093

now the standard error E is = (t*standard deviation)/sqrt(sample size)

E = (2.093*677)/sqrt(20) = 316.842

95% CI: 3120-E < u < 3120-E

95% CI: 3120-316.842 < u < 3120+316.842

95% CI: 2803.158 < u < 3436.842

We are 95% confident the annual earning mean is between 2803.158 and 3436.842

or (2803 , 3437) . Hence option B is correct