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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.

Respuesta :

Answer: It will reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Hypothesis:

[tex]H_0:\mu=288.5\\\\H_a:\mu\neq 288.5[/tex]

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.

[tex]t=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{289.7-288.5}{\dfrac{5.6}{\sqrt{24}}}\\\\t=1.05[/tex]

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

[tex]\alpha =1-0.95=0.05[/tex]

So, [tex]t_{\alpha ,df}=t_{0.05,23}=0.685[/tex]

Since t(calculated)>t

1.05>0.685

So, it will reject the null hypothesis.

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