Question

Seven students went on a diet in an attempt to lose weight, with two of them losing weight while all the others added weight. Is the diet is an effective way to losing weight α=1% (5mks)

Answer 1

Hypothesis.

Ho: Po≥0.5

Ha: Po<0.5

α =0.01

Test statistic.

t = $\frac{P-Po}{\sqrt{Po(1-Po)/n}}$

Rejection region.

The degrees of freedom =(n-1) =7-1=6. For 6 degrees of freedom and 0.01 alpha level of significance, the critical value from t distribution table t=-3.14 The decision is to reject the null hypothesis if the computed value t≤-3.14

t=$\frac{0.29 - 0.5}{\sqrt{0.5(1-0.5)/7}}$

=-1.11

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Decision.

Since the computed value t=-1.11>-3.14, we fail to reject the null hypothesis.

Conclusion.

At 1% level of significance, there is insufficient evidence to show that the diet is an effective way of losing weight