# Question: to test the effectiveness of a treatment a sample of...

###### Question details

To test the effectiveness of a treatment, a sample of *n*
= 36 people is selected from a normal population with mean of
*μ* = 60. After the treatment is administered to the
individuals in the sample, the sample mean is found to be
*M* = 55.

(a) If the population standard deviation is *σ* = 13, can
you conclude that the treatment has a significant effect? Use a
two-tailed test with *α* = 0.05. (Round your answers to two
decimal places.)

z-critical = |
± |

z = |

Conclusion:

a)Reject the null hypothesis, there is a significant treatment effect.

b)Fail to reject the null hypothesis, there is a significant treatment effect.

c)Fail to reject the null hypothesis, there is not a significant treatment effect.

d)Reject the null hypothesis, there is not a significant treatment effect.

(b) If the population standard deviation is *σ* = 19, can
you conclude that the treatment has a significant effect? Use a
two-tailed test with *α* = 0.05. (Round your answers to two
decimal places.)

z-critical = |
± |

z = |

Conclusion

Reject the null hypothesis, there is not a significant treatment effect.Fail to reject the null hypothesis, there is a significant treatment effect. Fail to reject the null hypothesis, there is not a significant treatment effect.Reject the null hypothesis, there is a significant treatment effect.

(c) Compute Cohen's *d* to measure effect size for both
tests (*σ* = 13 and *σ* = 19). (Round your answers to
two decimal places.)

σ =
13 |
d = |

σ =
19 |
d = |

(d) Briefly describe how the standard deviation influences the
outcome of the hypothesis test. How does *σ* influence
measures of effect size?

A)A larger standard deviation reduces the likelihood of
rejecting the null hypothesis, but has no effect on Cohen's
*d*.

B) larger standard deviation reduces the likelihood of rejecting the null hypothesis, but increases effect size.

C)A larger standard deviation reduces the likelihood of rejecting the null hypothesis and reduces effect size.

D)A larger standard deviation increases the likelihood of rejecting the null hypothesis, but reduces effect size.