Question

Consumer Reports tested 11 brands of vanilla yoghurt and found these numbers of calories per serving:

130 160 150 120 120 110 170 160 110 130 90

Use a 0.05 significance level to test the claim that the mean serving is equal to 120 calories, as a diet guide claim.

1. State the hypotheses and identify the claim

2. Find the critical value or values

3. Find the test statistic. First state the calculator command used to find it.  

4. Make the decision about the null hypothesis

5. Draw conclusion about the claim

Answer 1

Solution:

x	x2
130	16900
160	25600
150	22500
120	14400
120	14400
110	12100
170	28900
160	25600
110	12100
130	16900
90	8100
∑x=1450	∑x2=197500

Mean ˉx=∑xn

=130+160+150+120+120+110+170+160+110+130+90/11

=1450/11

=131.8182


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√197500-(1450)211/10

=√197500-191136.3636/10

=√6363.6364/10

=√636.3636

=25.2262

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 120

Ha :     120

Test statistic = t

= ( - ) / S / n

= (131.82-120) / 25.23 / 11

= 1.554

Test statistic = t = 1.554

P-value =0.1513

= 0.05  

P-value >  

0.1513 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that