The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor’s brand. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first 3 months after birth. The standard deviation of this sample is 2.3 pounds. A sample of 55 babies using the competitors brand revealed a mean increase of 8.8 pounds with a standard deviation of 2.9 pounds. At 95% level of confidence, can we conclude that the babies using the Gibbs product gained LESS weight? Z-test for Unpaired data

Question

The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor’s brand. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first 3 months after birth. The standard deviation of this sample is 2.3 pounds. A sample of 55 babies using the competitors brand revealed a mean increase of 8.8 pounds with a standard deviation of 2.9 pounds. At 95% level of confidence, can we conclude that the babies using the Gibbs product gained LESS weight? Z-test for Unpaired data

Answer 1

i am wanted the answer of this question

Answer 2

To determine whether the babies using the Gibbs product gained less weight than those using the competitor's product, we can perform a Z-test for unpaired data. This test allows us to compare the means of two independent samples.

Here are the steps to conduct the Z-test for unpaired data:

1. State the null hypothesis (H0) and the alternative hypothesis (HA):
H0: The mean weight gain of babies using the Gibbs product is equal to or greater than the mean weight gain of babies using the competitor's product.
HA: The mean weight gain of babies using the Gibbs product is less than the mean weight gain of babies using the competitor's product.

2. Determine the significance level (α) for your hypothesis test. In this case, we are conducting the test at a 95% confidence level, so α = 0.05.

3. Calculate the test statistic, which is a z-score formula for unpaired data:
z = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))
- x1 and x2 are the sample means of the Gibbs product and the competitor's product, respectively.
- s1 and s2 are the sample standard deviations of the Gibbs product and the competitor's product, respectively.
- n1 and n2 are the sample sizes of the Gibbs product and the competitor's product, respectively.

4. Find the critical value corresponding to the chosen significance level (α) and one-tailed test. Since the alternative hypothesis is less than, we use a one-tailed test in this case. You can look up the critical value from the Z-table or use a statistical software or calculator.

5. Compare the test statistic to the critical value. If the test statistic is less than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Now, let's calculate the test statistic:

x1 = 7.6 pounds (mean weight gain of babies using the Gibbs product)
s1 = 2.3 pounds (standard deviation of the Gibbs product sample)
n1 = 40 (sample size of the Gibbs product)

x2 = 8.8 pounds (mean weight gain of babies using the competitor's product)
s2 = 2.9 pounds (standard deviation of the competitor's product sample)
n2 = 55 (sample size of the competitor's product)

z = (7.6 - 8.8) / sqrt((2.3^2 / 40) + (2.9^2 / 55))

After calculating the value of z, compare it to the critical value at the 95% confidence level. If z is less than the critical value, you can conclude that the babies using the Gibbs product gained less weight.