Question

Each of 16 students measured the circumference of a tennis ball by four different methods, which were: A: Estimate the circumference by eye B: Measure the diameter with a ruler, then compute the circumference C: Measure the circumference with ruler and string D: Measure the circumference by rolling the ball along a ruler

Answer 1

Answer:

Following are the solution to the given equation:

Step-by-step explanation:

Please find the complete question in the attachment file.

In point a:

$\to \mu=\frac{\sum xi}{n}$

       $=22.8$

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

       $=\sqrt{\frac{119.18}{16-1}}\\\\ =\sqrt{\frac{119.18}{15}}\\\\ = \sqrt{7.94533333}\\\\=2.8187$

In point b:

$\to \mu=\frac{\sum xi}{n}$

       $=20.6875$  

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

       $=\sqrt{\frac{26.3375}{16-1}}\\\\=\sqrt{\frac{26.3375}{15}}\\\\ =\sqrt{1.75583333}\\\\ =1.3251$

In point c:

 $\to \mu=\frac{\sum xi}{n}$

         $=21$  

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

       $=\sqrt{\frac{2.62}{16-1}}\\\\ =\sqrt{\frac{2.62}{15}} \\\\= \sqrt{0.174666667}\\\\=0.4179$

In point d:

$\to \mu=\frac{\sum xi}{n}$

       $=20.8375$  

$\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}$

       $=\sqrt{\frac{8.2975}{16-1}}\\\\ =\sqrt{\frac{8.2975}{15}} \\\\ =\sqrt{0.553166667} \\\\ =0.7438$