Question

view PUllies Current Attempt in Progress How Big Are Gribbles? Gribbles are small, pale white, marine worms that bore through wood. While sometimes considered a pest since they can wreck wooden docks and piers, they are now being studied to determine whether the enzyme they secrete will allow us to turn inedible wood and plant waste into biofuel. A sample of 50 gribbles finds an average length of 3.1 mm with a standard deviation of 0.72. Give a best estimate for the length of gribbles, a margin of error for this estimate (with 95% confidence), and a 95% confidence interval. Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places. point estimate = i margin of error = i The 95% confidence interval is i to i 1Sanderson, K., "A Chewy Problem," Nature, 23 June 2011, p. 512. e Textbook and Media Attempts: 0 of 3 used Save for Later Submit Answer Send to Gradebook

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 3.1

sample standard deviation = s = 0.72

sample size = n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,49 = 2.010

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.010 * (0.72 / $\sqrt$50)

= 0.20

The 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

3.1 - 0.20 < $\mu$ < 3.1 + 0.20

2.90 < $\mu$ < 3.30

The 95% confidence interval is 2.90 to 3.30