A gymnastics coach uses a new technique to train a random selection of 7 gymnasts on the balance beam. The balance beam scores for the gymnasts were recorded in a competition before the technique was used and recorded in a competition after the technique was used. A dependent samples t-test at a significance level of 0.01 was used to test the claim that this new technique is effective in raising the balance beam scores of these gymnasts. The test statistic is -0.880 and the critical value is -3.143. What is the conclusion of the test? Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the technique is effective in raising scores.
Added by Alexander J.
Step 1
The null hypothesis (H0) is that the new technique has no effect on the balance beam scores of the gymnasts. The alternative hypothesis (H1) is that the new technique is effective in raising the balance beam scores of the gymnasts. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Dominador Tan and 77 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts, using a scale from 1 to 10, where 10 is a perfect score. A statistician wants to see if the gymnasts (Factor A) differ in their performances and also wants to see if the scores vary significantly across judges (Factor B) in order to assess any bias in the judges. To do this the statistician uses a two-way ANOVA without interaction and the results are show below. Gymnast (Factor A) Judge (Factor B) Gymnast 1 Gymnast 2 Gymnast 3 Gymnast 4 Gymnast 5 Factor B MEANS Judge 1 8.0 9.5 7.3 8.3 8.8 8.38 Judge 2 8.5 9.2 7.5 8.7 9.2 8.62 Judge 3 8.2 9.7 7.7 8.5 9.0 8.62 Factor A MEANS 8.23 9.47 7.50 8.50 9.00 Source of Variation SS df MS F p-value Critical Value Rows (Factor B) 0.192 2 0.139 Columns (Factor A) 6.743 4 0.000 Error 0.301 8 Total 7.236 14 At 0.05 level of significance, which of the following conclusions can be made? Select one: There is evidence that the judges differ in their scoring (are biased), therefore, blocking on judges is necessary to control for those differences. Also, when controlling for differences in judges, there is no evidence that the gymnasts differ in their scores. There is no evidence that the judges differ in their scoring (or are biased), therefore, there is no need for blocking on judges. Also, there is evidence that the gymnasts differ in their scores. There is evidence that the judges differ in their scoring (are biased), therefore, blocking on judges is necessary to control for those differences. Also, when controlling for differences in judges, there is evidence that the gymnasts differ in their scores. There is no evidence that the judges differ in their scoring (or are biased), therefore, there is no need for blocking on judges. Also, there is no evidence that the gymnasts differ in their scores.
Dominador T.
At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts, using a scale from 1 to 10, where 10 is a perfect score. A statistician wants to see if the gymnasts (Factor A) differ in their performances and also wants to see if the scores vary significantly across judges (Factor B) in order to assess any bias in the judges. To do this the statistician uses a two-way ANOVA without interaction and the results are show below. Gymnast (Factor A) Judge (Factor B) Gymnast 1 Gymnast 2 Gymnast 3 Gymnast 4 Gymnast 5 Factor B MEANS Judge 1 7.6 9.1 6.7 8.0 8.4 7.96 Judge 2 8.5 9.2 7.5 8.7 9.9 8.76 Judge 3 8.2 9.9 9.5 9.5 9.2 9.26 Factor A MEANS 8.10 9.40 7.90 8.73 9.17 Source of Variation SS df MS F p-value Critical Value Rows (Factor B) 4.3 2 0.027 Columns (Factor A) 5.103 4 0.062 Error 2.913 8 Total 12.316 14 What is the F-test statistic for testing differences in mean scores across the Gymnasts? (NOTE: do not round numbers until the last step to avoid rounding errors) 2.549 44.752 3.504 5.904 24.053
Madhur L.
Elite Gymnastics, Women ~ After the 2004 Olympic games, the scoring system for gymnastics was overhauled. Rather than rank performances from 0 points to 10 points as the old system did, the new system judges routines based on a combination of the difficulty of the skills attempted in the performance and the gymnast’s execution of the skills.One result of this change is that the distribution of scores for elite gymnasts at international competitions now closely resembles the normal curve.Female gymnasts compete on four different apparatus: Vault, Floor, Uneven Bars, and Balance Beam. The values given in this problem were calculated from the reported results of international competitions of female elite gymnasts between the years 2006 and 2019.Scores on the Floor apparatus follow a normal distribution with a mean of 14.399 and a standard deviation of 0.635Round all calculated answers to 4 decimal places.1. What proportion of female elite gymnasts score between 12.945 and 15.021 on the Floor apparatus? 2. What proportion of female elite gymnasts score lower than 13.421 on the Floor apparatus? 3. Suppose a female elite gymnast scored 14.126 on the Floor apparatus. What proportion of gymnasts scored higher than she did? 4. Keisha wants to follow on Instagram all the elite gymnasts who score in the top 8% on the Floor apparatus. How high would an elite gymnast need to score in order for Keisha to want to follow her on Instagram?
Kari H.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD