before and after using the newly designed clubs. Step 1 of 5:State the null and alternative hypotheses for the test. Step 2 of 5:Find the value of the standard deviation of the
before and after using the newly designed clubs. Step 1 of 5:State the null and alternative hypotheses for the test. Step 2 of 5:Find the value of the standard deviation of the
before and after using the newly designed clubs. Step 1 of 5:State the null and alternative hypotheses for the test. Step 2 of 5:Find the value of the standard deviation of the
A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim? Let d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs) d = (golf score after using the newly designed golf clubs) − (golf score before using the newly designed golf clubs) . Use a significance level of α=0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs.
Step 1 of 5:State the null and alternative hypotheses for the test.
Step 2 of 5:Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
Step 3 of 5:Compute the value of the test statistic. Round your answer to three decimal places.
Step 4 of 5:Find the p-value for the hypothesis test. Round your answer to four decimal places.
Step 5 of 5:Draw a conclusion for the hypothesis test.
Transcribed Image Text:The text consists of four statements regarding hypothesis testing in the context of a golf club manufacturer's claim:
1. **Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, to support the golf club manufacturer's claim.**
2. **Reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, to support the golf club manufacturer's claim.**
3. **Fail to reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, to support the golf club manufacturer's claim.**
4. **Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, to support the golf club manufacturer's claim.**
Each statement reflects a different conclusion that can be drawn from hypothesis testing concerning the level of significance (0.05) used in statistical analysis.
Transcribed Image Text:### Golf Score Comparison Table
This table presents a comparison of scores from golfers using two different golf designs. The first row displays the scores from the old design, and the second row shows scores from the new design.
| Golfer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-------------------------------|----|----|----|----|----|----|----|----|
| **Score (old design)** | 88 | 75 | 93 | 77 | 80 | 79 | 76 | 83 |
| **Score (new design)** | 81 | 78 | 89 | 74 | 82 | 75 | 72 | 76 |
- **Golfer 1** improved from 88 (old) to 81 (new).
- **Golfer 2** saw a slight increase from 75 to 78.
- **Golfer 3** reduced their score from 93 to 89.
- **Golfer 4** decreased their score from 77 to 74.
- **Golfer 5** increased from 80 to 82.
- **Golfer 6** reduced their score from 79 to 75.
- **Golfer 7** lowered their score from 76 to 72.
- **Golfer 8** had a slight decrease from 83 to 76.
This data can be used to analyze the effectiveness of the new design in improving golfers' performance.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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