Question

Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: $8;8;10;7;9;9$. Assume the underlying distribution is approximately normal.

a. Construct a $90\%$confidence interval for the population mean grams of fat per serving of chocolate chip cookies

sold in supermarkets.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?

c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.

d. Calculate the mean.

e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?

Short answer

(a) The final results are:

1.$CI=(5740.1,7109.9)$

2. through graph we see that

3.$EBM=665.0178$.

(b) If you desired a lower error bound while maintaining the same degree of confidence, you should have raised the sample size.

(c) The data recorded is we see is given below,

Fats per serving $=9,11,10,11,7,7$

(d) Mean is $\overline{x}=9.1667.$

(e) Yes, the above-mentioned mean falls inside the confidence interval because the sample is so tiny that it does not usually provide reliable results.

Step-by-step solution

Explanation (a)

i. Using the $TI-83$calculator or the $TI-83,83+,84,84+$calculators, state the confidence interval.

Make a list of the information.

Press STAT button and then arrow $\to$to TESTS.

Arrow $\downarrow$to $8:T$Interval.

Press ENTER button.

Arrow to $\to$and press ENTER.

Arrow $\downarrow$and enter the name of the list where the data is stored.

Enter Freq : 1 Enter $\mathit{C}$- Level : $.9$

Arrow $\downarrow$to

Calculate and hit the Enter key.

The confidence interval's output,

$CI=(5740.1,7109.9)$

ii. The graph is as follows:

iii. The formula is used to compute the error bound.

$EBM=t_{n-1}\left(\frac{a}{2}\right)\frac{s}{\sqrt{n}}$

$EBM=t_{84-1}\left(\frac{0.05}{2}\right)\frac{3156}{\sqrt{84}}$

$EBM=665.0178$.

Explanation (b)

If you desired a lower error bound while maintaining the same degree of confidence, you should have raised the sample size.

Explanation (c)

The data recorded is we see is given below,

Fats per serving $=9,11,10,11,7,7$.

Explanation (d)

Here we calculate mean is,

$\overline{x}=\frac{9+11+10+11+7+7}{6}$

$\overline{x}=9.1667.$

Explanation (e) 

Yes, the above-mentioned mean falls inside the confidence interval because the sample is so tiny that it does not usually provide reliable results.