Question

Frito-Lay fills bags of tortilla chips that are labeled with a net weight of 288.5 grams. A random sample of 24 bags is selected and found to have an average net weight of 289.7 grams and a sample standard deviation of 5.6 grams. Use a 95% confidence interval to investigate whether the filling process is working properly.

Answer 1

Answer: It will reject the null hypothesis.

Explanation:

Since we have given that

Hypothesis:

`H_0:\mu=288.5\\\\H_a:\mu\\eq 288.5`

n = 24

Average mean = 289.7 grams

Standard deviation = 5.6 grams

We need to find the 95% confidence interval.

Since n = 24 <30 , so we will use t test.

`t=\frac{\bar{x}-\mu}{(\sigma)/(√(n))}\\\\t=(289.7-288.5)/((5.6)/(√(24)))\\\\t=1.05`

Now, degrees of freedom = n- 1 = 24-1 =23

`\alpha =1-0.95=0.05`

So,
`t_(\alpha ,df)=t_(0.05,23)=0.685`

Since t(calculated)>t

1.05>0.685

So, it will reject the null hypothesis.