Question

Fruit fly thorax lengths Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) was measured for each fly in a random sample of $49$male fruit flies. The mean length was $\overline{x}=0.8004\mathrm{mm}$, with a standard deviation of $s_X=0.0782\mathrm{mm}$mm. Construct and interpret a $90\%$confidence interval for the true mean thorax length of a male fruit fly.

Short answer

Required confidence interval is$(0.7817,0.8191)$

Step-by-step solution

Given Information

It is given that $n=14$

$\left(\overline{x}\right)=0.8004$

$\left(s_x\right)=0.0782$

Concept Used

Formula to be used is$\overline{x}-t_{\frac{a}{2},n-1}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\frac{a}{2},n-1}\times \frac{s}{\sqrt{n}}$

Calculation

• In MINTAB Sheet, enter data set.
• Press Stat>Basic Statistics>1-Sample t.
• Choose summarized data. Enter given values.
• Check options and enter $90\%$in confidence level.
• Press OK.

Output obtained is:

Confidence Interval is $(0.7817,0.8191)$

There is $95\%$confidence that true mean length lies between$0.7817\text{and}0.8191$