Question

Many food manufacturers fortify their food products by adding vitamins. The following data are the amounts of vitamin C measured in mg/100g of corn soy blend for a random sample of size 8.

Sample points: 26   31   23   22   11   22   14   31

The US Agency for International Development specifies a mean vitamin C content of 30 mg. Test the hypothesis that mean vitamin C content does not conform to these specifications at significance level 5%.

(s=7.19)

Decision:                             [ Select ]                       ["Reject the null hypothesis.", "Do not reject the null hypothesis."]      

Answer 1

Solution:

x	x2
26	676
31	961
23	529
22	484
11	121
22	484
14	196
31	961
∑x=180	∑x2=4412

Mean ˉx=∑xn

=26+31+23+22+11+22+14+31/8

=180/8

=22.5

= 30

=22.5

S =7.19

n = 8

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 30

Ha :     30

Test statistic = t

= ( - ) / S / n

= (22.5-30) / 7.19 / 8

= −2.95

Test statistic = t =  −2.95

P-value =0.0214

= 0.05  

P-value <

0.0214 < 0.05

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is different than 30, at the 0.05 significance level.