A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $H0\mathrm { H } _ { 0 }$ : p = 0.72; $HA\mathrm { H } _ { \mathrm { A } }$ : p ? 0.72; z = 1.58; P-value = 0.1236.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should not continue with this strategy.
B) $H0\mathrm { H } _ { 0 }$ : p = 0.72; $HA\mathrm { H } _ { \mathrm { A } }$ : p > 0.72; z = 1.58; P-value = 0.0571.This data shows moderate evidence of a weight loss in more than 72% of the participants in the weight loss strategy; it is hard to say whether or not they should use this strategy,perhaps further testing is in order.
C) $H0\mathrm { H } _ { 0 }$ : p = 0.72; $HA\mathrm { H } _ { \mathrm { A } }$ : p > 0.72; z = -1.58; P-value = 0.0618.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should change strategies.
D) $H0\mathrm { H } _ { 0 }$ : p = 0.72; $HA\mathrm { H } _ { \mathrm { A } }$ : p < 0.72; z = -1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.
E) $H0\mathrm { H } _ { 0 }$ : p = 0.72; $HA\mathrm { H } _ { \mathrm { A } }$ : p < 0.72; z = 1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.

Question

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A)

H0\mathrm { H } _ { 0 }

: p = 0.72;

HA\mathrm { H } _ { \mathrm { A } }

: p ? 0.72; z = 1.58; P-value = 0.1236.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should not continue with this strategy.
B)

H0\mathrm { H } _ { 0 }

: p = 0.72;

HA\mathrm { H } _ { \mathrm { A } }

: p > 0.72; z = 1.58; P-value = 0.0571.This data shows moderate evidence of a weight loss in more than 72% of the participants in the weight loss strategy; it is hard to say whether or not they should use this strategy,perhaps further testing is in order.
C)

H0\mathrm { H } _ { 0 }

: p = 0.72;

HA\mathrm { H } _ { \mathrm { A } }

: p > 0.72; z = -1.58; P-value = 0.0618.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should change strategies.
D)

H0\mathrm { H } _ { 0 }

: p = 0.72;

HA\mathrm { H } _ { \mathrm { A } }

: p < 0.72; z = -1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.
E)

H0\mathrm { H } _ { 0 }

: p = 0.72;

HA\mathrm { H } _ { \mathrm { A } }

: p < 0.72; z = 1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.

Aubrey Aguilor · Accepted Answer

Final Answer : B, Explanation :  The null hypothesis is that the proportion of weight loss in the population (p) is equal to 0.72, while the alternative hypothesis is that p is greater than 0.72. The sample proportion from the random sample of 140 participants is 0.78.Since the sample size is large (n=140), we can assume that the sampling distribution of the sample proportion is approximately normal by the central limit theorem.Using a one-sided z-test with a 0.05 level of significance, we get a z-score of 1.58 and a p-value of 0.0571.Since the p-value is greater than 0.05, we fail to reject the null hypothesis. This means that the evidence is not strong enough to conclude that the weight loss strategy is better than the previous strategy. Therefore, further testing may be required before making any decisions.

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