Gibbs Baby Food Company Wants To Compare Weight Gain

Gibbs Baby Food Company Wishes To Compare the Weight Gain Of Infants U

Gibbs Baby Food Company wants to compare the weight gain of infants using its brand versus its competitor's. A sample of 40 babies using Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth, with a population standard deviation of 2.3 pounds. A sample of 55 babies using the competitor's brand revealed a mean increase of 8.1 pounds, with a population standard deviation of 2.9 pounds. The research aims to test whether the mean weight gain for Gibbs is less than that of the competitor, at a 0.05 significance level.

The hypotheses are:

  • Null hypothesis (H0): μG ≥ μC
  • Alternative hypothesis (H1): μG

The decision rule states that at a significance level of 0.05, we reject H0 if the calculated z-statistic is less than -1.645 (the critical value for a one-tailed test).

To compute the test statistic, we use the formula for the z-test for two population means with known standard deviations:

z = (X̄G - X̄C) / √(σG² / nG + σC² / nC)

where:

  • X̄G = 7.6
  • X̄C = 8.1
  • σG = 2.3
  • σC = 2.9
  • nG = 40
  • nC = 55

Calculating the denominator:

√(2.3² / 40 + 2.9² / 55) = √(5.29 / 40 + 8.41 / 55) = √(0.13225 + 0.15291) = √0.28516 ≈ 0.534

Calculating the numerator:

7.6 - 8.1 = -0.5

Thus, the test statistic:

z = -0.5 / 0.534 ≈ -0.936

The p-value associated with z = -0.936 for a one-tailed test can be found using standard normal distribution tables or software, which is approximately 0.1740.

Since the p-value (0.1740) exceeds the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that babies using the Gibbs brand gained less weight than those using the competitor's.

Sample Paper For Above instruction

Understanding the comparative effectiveness of baby foods through statistical analysis is pertinent for manufacturers aiming to demonstrate the benefits of their products. In this study, we examine whether Gibbs Baby Food Company’s product leads to less weight gain in infants than a competing brand, utilizing hypothesis testing methods grounded in statistical inference. The purpose of this analysis is to assess if the observed mean differences are statistically significant within the context of a 0.05 significance level, thereby informing product positioning and health claims.

The problem involves two independent samples: one from infants consuming Gibbs baby food and another from those consuming a competitor's. The sample sizes are 40 and 55, respectively. The mean weight gains are 7.6 pounds for Gibbs and 8.1 pounds for the competitor. Population standard deviations are known, which simplifies the testing procedure to a z-test for two means with known variances. This approach is appropriate because the large sample sizes justify the assumption of normality and the use of known population standard deviations.

The hypotheses are explicitly set to determine if Gibbs’s product results in lesser weight gain, with the null stating no difference or a higher gain from Gibbs (μG ≥ μC), and the alternative focusing on Gibbs being less effective (μG

Calculating the test statistic involves substituting the sample means, known standard deviations, and sample sizes into the z-test formula. The resulting z-value of approximately -0.936 is compared against the critical value. The corresponding p-value of about 0.174 surpasses 0.05, indicating a lack of statistical significance. Consequently, we do not reject the null hypothesis and conclude that there is no sufficient evidence to assert that Gibbs’s product causes less weight gain compared to the competitor.

This outcome emphasizes the importance of rigorous statistical testing in validating health and marketing claims. Although the mean weight gain with Gibbs appears slightly lower, the difference is not statistically significant based on the current sample data. Future research could explore larger sample sizes or other metrics to further validate these findings, reinforcing the necessity of evidence-based product claims in the infant nutrition industry.

In conclusion, applying hypothesis testing in the context of comparative infant weight gain provides valuable insights for both researchers and manufacturers. It illustrates how statistical methods can objectively evaluate product efficacy, ultimately guiding marketing strategies and contributing to consumer trust. While current data does not show a significant difference, the process underscores the importance of precision and rigor in scientific inquiry.

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