Question

At the Olympic-level of competition, even the smallest factors can make the difference between winning and losing. For example, Pelton (1983) has shown that Olympic markspersons shoot much better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat. The small vibration caused by a heartbeat seems to be sufficient to affect aim. A sample of n=12 Olympic markspersons fires a series of rounds while a researcher records heartbeats. For each marksperson, a scores is recorded for shots fired during heartbeats and for shots fired between heartbeats.

the following is data I received of the scores in a paired t-test.

during heartbeats score mean = 92, standard deviation = 1.71; between heartbeats mean= 94, standard deviation = 2.73; t - statistic = -5.14, df= 11, p-value = p < 0.001.

The question:

1. Define the null and make a decision about it by doing the following:

a) Using words and specific values (e.g. not something like “μ₁ = μ₂”), report the specific null hypothesis for this study.

b) Write out your decision about the null: “I [reject OR fail to reject] the null …”

c) Write out your rationale for that decision: “… because [p < .05 OR p > .05]”

Please provide a detailed explanation to this null report, include all the criteria. I am having a difficult time establishing when I need to reject or fail to reject the hypothesis and how I would know to.

Answer 1

Sol:

From words:

better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat

1. Define the null and make a decision about it by doing the following:

a) Using words and specific values (e.g. not something like “μ₁ = μ₂”), report the specific null hypothesis for this study.

Null hypothesis:

Ho:

where  mu1=mean score during heartbeats,

mu2=mean score between heartbeats,

Ho means there is no difference in mean scores during and between heart beats

Alternative hypothesis:

Ha:

Ho means there mean scores during heartbeats is less than squeezing the trigger during a heartbeat

b) Write out your decision about the null: “I [reject OR fail to reject] the null …”

here no alpha is mentioned

alpha=0.05

p we got is

p < 0.001

compare alpha and p to decide

0.001<0.05

p<0.05

Reject null hypothesis

Accept alternative hypothesis

c) Write out your rationale for that decision: “… because [p < .05 OR p > .05]”

p<0.05

There is sufficient statistical evidence at 5% level of significance to conclude that

fire between heartbeats are better than squeezing the trigger during a heartbeat.