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Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor's. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. For the Gibbs brand, the population standard deviation of the sample is 2.3 pounds. A sample of 55 babies using the competitor's brand revealed a mean increase in weight of 8.1 pounds. The population standard deviation is 2.9 pounds.

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Answer:

Mean weight gained of two goods is not significantly different under 0.05 or 0.01 significance level, but it is under 0.10 significance level.

Step-by-step explanation:

We need to calculate the z-statistic of the differences of sample means and compare if it is significant under a significance level.

Z-score can be calculated using the formula:

z=[tex]\frac{X-Y}{\sqrt{\frac{s(x)}{N(x)}+\frac{s(y)}{N(y)}}}[/tex] where

  • X is the mean weight gain for in the first three months after birth for babies using the Gibbs products.
  • Y is the mean weight gain for in the first three months after birth for babies using the competitor products
  • s(x) is the population standard deviation of the sample for Gibbs brand
  • s(y) is the population standard deviation of the sample for competitor brand
  • N(x) is the sample size for babies used Gibbs product
  • N(y) is the sample size for babies used competitor product.

putting the numbers in the formula:

z=[tex]\frac{7.6-8.1}{\sqrt{\frac{2.3}{40}+\frac{2.9}{55}}}[/tex] ≈ -1.51

and z-table gives that P(z<-1.51) = 0.0655

To conclude if the competitor good is significantly better, we need to choose a significance level and compare it to 0.0655.

For example, the difference in mean weight gained of two goods is not significant under 0.05 or 0.01 significance since 0.0655 is bigger than these values. But we can conclude that under 0.10 significance, competitor brand mean weight gain is significantly more than the Gibbs brand mean weight gain.  

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