Question

1,500 women followed the Atkin’s diet for a month. A random sample of 30 women gained an average of 6.7 pounds. The Atkin announces that the average weight gain per woman for the month was 6 pounds. The standard deviation for the sample was 9.0. We want to test whether the Atkin’s announcement was correct. Use 5% significance level, conduct the corresponding t-test

a) state the null/alternative hypothesis
b) construct the test statistic
c) state the distribution that the statistic follows
d) calculate the corresponding p-value
e) state the conclusion

Answer 1

To test the correctness of the Atkins announcement about average weight gain, a t-test needs to be conducted using the given sample data. The null and alternate hypotheses, test statistic, distribution, p-value, and conclusion can be determined by the t-test.

Step-by-step explanation:

To test whether the Atkins announcement about average weight gain was correct, we need to conduct a t-test.

a) Null hypothesis: The average weight gain per woman for the month was 6 pounds. Alternate hypothesis: The average weight gain per woman for the month was different from 6 pounds.

b) Test statistic: t = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size))

c) The test statistic follows a t-distribution with degrees of freedom = Sample Size - 1

d) Calculate the corresponding p-value using the t-distribution table or a calculator.

e) State the conclusion: If the p-value is less than the significance level (5% in this case), we reject the null hypothesis and conclude that the average weight gain per woman for the month was different from 6 pounds. Otherwise, we fail to reject the null hypothesis.