Question

3. Nelson's Foods wishes to compare the weight gain of infants using its brand versus their competitor's. A sample of 90 babies using Nelson's product revealed a mean weight gain of 7.6 pounds in the first three months. The population standard deviation for Nelson's brand was 2.3 pounds. A random sample of 105 babies using the competitor's brand revealed a mean weight gain of 8.2 pounds with a population standard deviation of 2.9 pounds. At the 6% significance level, can you conclude that babies using Nelson's brand gain less weight?

Answer 1

Let sample 1 is sample of babies using Nelson's product and sample 2 is sample of the competitor's brand.

So we have : n1 = 90, = 7.6, = 2.3 , n2 = 105, = 8.2, = 2.9 , = 0.06

Claim : Babies using Nelson's brand gain less weight.

So the hypothesis are :

H0: v/s H1 :

Here population standard deviations are known . Sample sizes are also greater than 30. Hence we use here z test statistic.

The test statistic is,

  

= -1.61

p value = p ( z < -1.61 )

= 0.0537

Here p value < ( 0.06). Hence we reject null hypothesis.

Conclusion :

There is sufficient evidence to support the claim that babies using Nelson's brand gain less weight.