Question

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 101 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Answer 1

The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).

Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.

From the given information,

Let n=101 represents the size of the sample.

Let $\bar{x}$= 12.9 represents the mean of the sample.

Let s= 3.2 represents the standard deviation of the sample.

Degrees of freedom:

df = n-1

df= 101-1

df= 100

The critical value of t at 0.2 level of significance with 100 degrees of freedom is,

$\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end$

The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:

$\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end$

Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).

Learn more about confidence intervals from here brainly.com/question/15969219

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