Question

It is desired to test the claim that a steady diet of eggs will cause people to lose 10 lbs over 5 months. A random sample of 49 people was taken yielding an average weight loss over 5 months of 9.7 pounds, with Sx = 2.5 lbs. Use a two tailed test and at α =.02 to determine the validity of the weight loss claim.

Answer 1

The null and alternate hypothesis are:

H0: $\mu=10$

Ha: $\mu\neq 10$

The test statistic is given by:

$Z=\frac{\overline{x}-\mu}{\frac{S}{\sqrt{n}}}=\frac{9.7-10}{\frac{2.5}{\sqrt{49}}}=-0.84$

Since this is a two-tailed test, so the p-value is given by:

$\\2\times P(Z<-0.84)=2\times P(Z>0.84)=2\times [1-P(Z<0.84)]\\ \\ =2\times [1-0.79955]=0.4009$

Since p-value is greater than 0.02, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus we can conclude that $\mu=10$ i.e. the claim is valid.