Let\'s suppose we run a company that manufactures baby food. It is essential tha

Question

Let's suppose we run a company that manufactures baby food. It is essential that the preparation have 100 calories per serving. We sample 225 batches and test the calorie content. Our sample statistics are x=96 and s=30.
We need to test H0: =100 against the alternative HA: <100.

If we use a significance level of 0.05, the following picture shows you the rejection region and critical values for the test.

The picture shows a t-distribution with the area to the left of the number -1.652 shaded (total shaded area equals 0.05).

For Blank 1, calculate the test statistic, using the formula

T=x¯s/N

and two decimal places.

Type "yes" in Blank 2 if we should reject H0; type "no" in Blank 2 if we should fail to reject H0.

Find the p-value for this statistic using a t-distribution with 224 degrees of freedom.

Calculate the p-value of the test statistic using Graph>Probability Distribution> and choose the t-distribution with 224 degrees of freedom. Click on the radio button that says "X" and type in your response to Answer 1 (Answer 1 is your "X" value here). Put the p-value into Blank 3 (five decimal places).

Would we reject at the 1% significance level? Type "yes" for reject and "no" for fail to reject in Blank 4.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   100  
Ha:    u   <   100  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    224          
tcrit =    -   1.65168456      
              
Getting the test statistic, as              
              
X = sample mean =    96          
uo = hypothesized mean =    100          
n = sample size =    225          
s = standard deviation =    30          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2   [ANSWER, TEST STATISTIC]

********************************************      
              
              
Comparing t and tcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS. [ANSWER: YES]

***********************************          

Also, the p value is              
              
p =    0.02335 [ANSWER]

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Would we reject at the 1% significance level? Type "yes" for reject and "no" for fail to reject in Blank 4.

As P > 0.01, we dail to reject Ho. [ANSWER: NO]      

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