Can you become addicted to exercise? In a study conducted to...

Can you become addicted to exercise? In a study conducted to answer this question, a random sample of dedicated exercisers, who usually work out every day, was drawn. Each completed a questionnaire that gauged their mood on a fivepoint scale, where $5=$ very relaxed and happy, $4=$ somewhat relaxed and happy, $3=$ neutral feeling, 2 = tense and anxious and 1 = very tense and anxious. The group was then instructed to abstain from all workouts for the next three days. Moreover, they were told to be as physically inactive as possible. Each day their mood was measured using the same questionnaire. Column 1 stores the code identifying the respondent, and columns 2 to 5 store the measures of mood for the day before the experiment began and for the three days of the experiment, respectively. a Can we infer that for each day the exercisers abstained from physical activity, they were less happy than when they were exercising? b Do the data indicate that by the third day moods were improving? c Draw two possible conclusions from your findings. Sample statistics: a Before Day 1: $n$ (positive $)=67$, $n$ (negative $)=0, n($ zero $)=5$; Day $2: n$ (positive $)=59$, $n($ negative $)=0, n($ zero $)=13$; Day $3: n$ (positive $)=35$, $n$ (negative $)=0, n($ zero $)=37$. b Day 2 Day $3: n$ (positive) $=3, n$ (negative $)=37$, $n($ zero $)=32$.

Can you become addicted to exercise? In a study conducted to answer this question, a random sample of dedicated exercisers, who usually work out every day, was drawn. Each completed a questionnaire that gauged their mood on a fivepoint scale, where $5=$ very relaxed and happy, $4=$ somewhat relaxed and happy, $3=$ neutral feeling, 2 = tense and anxious and 1 = very tense and anxious. The group was then instructed to abstain from all workouts for the next three days. Moreover, they were told to be as physically inactive as possible. Each day their mood was measured using the same questionnaire. Column 1 stores the code identifying the respondent, and columns 2 to 5 store the measures of mood for the day before the experiment began and for the three days of the experiment, respectively.
a Can we infer that for each day the exercisers abstained from physical activity, they were less happy than when they were exercising?
b Do the data indicate that by the third day moods were improving?
c Draw two possible conclusions from your findings.
Sample statistics:
a Before Day 1: $n$ (positive $)=67$,
$n$ (negative $)=0, n($ zero $)=5$; Day $2: n$ (positive $)=59$,
$n($ negative $)=0, n($ zero $)=13$; Day $3: n$ (positive $)=35$,
$n$ (negative $)=0, n($ zero $)=37$.
b Day 2 Day $3: n$ (positive) $=3, n$ (negative $)=37$, $n($ zero $)=32$.

Key Concepts

Hypothesis Testing

Hypothesis testing is a method used to evaluate the evidence provided by data in relation to a specific claim or hypothesis. By comparing observed data against a null hypothesis, researchers determine whether there is statistically significant evidence to support an alternative hypothesis, thus allowing for data-driven conclusions.

Statistical Inference

Statistical inference is the process of drawing conclusions about a population based on sample data. It involves using summary statistics, sample distributions, and hypothesis testing to infer whether observed effects are likely due to chance or reflect a true underlying phenomenon.

Pretest-Posttest Comparison

Pretest-posttest comparison involves measuring the same subjects before and after an intervention to observe changes attributable to that intervention. This method provides a framework for assessing the impact of the experimental manipulation by comparing baseline measurements with subsequent observations.

Within-Subjects Design

Within-subjects design is an experimental approach where the same participants are observed under different conditions or over different time points. This design allows researchers to compare results from the same individuals, thus controlling for many extraneous variables that might otherwise influence the outcome.

Random Sampling

Random sampling is a technique used to select study participants in such a way that each member of the target population has an equal chance of being chosen. This method helps minimize potential biases in the selection process, improving the generalizability of the results to the broader population.

Study Design

Study design refers to the overall strategy that is used to integrate the different components of the study in a coherent and logical way, ensuring that the research problem is effectively addressed. It encompasses the methods for selecting subjects, manipulating variables, and collecting data, and it plays a critical role in determining the validity and reliability of the study's conclusions.

Transcript

00:01 So we have a study designed to see what type of incentive might be most effective in encouraging people to exercise.

00:08 So in this study, we had 281 overweight or obese people, and they were assigned the goal to walk 7 ,000 steps a day, and their activity was tracked for 100 days.

00:23 The participants were randomly assigned to one of four groups.

00:27 So we had group one, group two, group three, and group four.

00:38 And again, we had a total of 281 participants.

00:46 In this problem, we look at the overall success rate.

00:51 For each participant, we recorded the number of days that the participant met the goal.

00:57 For all 281 participants, the average cost.

01:03 Goal was 36 .5.

01:11 So that means out of the 100 days they exercised for 36 .5 days on average.

01:19 The standard error for this estimate was 1 .80.

01:28 And we need to test to see if this provides evidence that the mean number of days meeting the goal for the people in this, this 100 -day program to encourage exercise is greater than 35.

01:49 So that's what we're trying to test.

01:51 So the first thing we need to do is to construct our null and alternative hypotheses.

01:58 And since what we are testing is an inequality, that would represent the alternative hypothesis.

02:06 The null hypothesis must be a statement of equality.

02:10 So we would say mu is equal.

02:13 To 35.

02:15 Now based on the alternative hypothesis, we know that this is going to be a right -tailed test because of the inequality greater than.

02:27 So we are going to first find our standardized test statistic, and then we're going to find our p value.

02:35 To find our standardized test statistic, we are going to apply the formula x bar minus mu, over the standard area, or sorry, standard error.

02:50 So our standardized test statistic will be 36 .5, which is taken from our sample minus what we state in our null hypothesis.

03:05 We said that m would equal 3 or 35, and we'll divide it by our standard error of 1 .80.

03:14 In doing so, we do get a, a z standardized test statistic to be .833.

03:26 So now we want to find our p value, and our p value is going to be this area that extends into the right tail.

03:37 And in order to find that p value, we are going to use our stat key app...

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