half is in another. Please provide t critical value, t calculated value, and if you rejected or accepted the null hypothesis that ponds have lower hardnes

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Please answer question 9.16 half of the question is in one photo and half is in another. Please provide t critical value, t calculated value, and if you rejected or accepted the null hypothesis that ponds have lower hardness
The image contains text from a page discussing statistical values and concepts relating to water hardness in Kansas. Here's the transcription of the visible portion:

"9.16 Suppose that the mean water hardness of lakes in Kansas is 425 mg/L, and these values tend to follow a normal distribution."

The page also contains a vertical list of numerical values, which appears to resemble data points or statistical values. Due to the orientation and limited view, only partial context is available. 

This extract might be from a textbook focused on statistics or environmental science, discussing real-world applications of statistical distributions.
Transcribed Image Text:The image contains text from a page discussing statistical values and concepts relating to water hardness in Kansas. Here's the transcription of the visible portion: "9.16 Suppose that the mean water hardness of lakes in Kansas is 425 mg/L, and these values tend to follow a normal distribution." The page also contains a vertical list of numerical values, which appears to resemble data points or statistical values. Due to the orientation and limited view, only partial context is available. This extract might be from a textbook focused on statistics or environmental science, discussing real-world applications of statistical distributions.
**The Paired t-Test**

The following data are for pre-exercise and post-exercise body temperature measurements for eight young adults. Is there a difference in mean body temperature following exercise?

- **Individual Number**: 1, 2, 3, 4, 5, 6, 7, 8
- **Resting**: 994, 291, 360, 385, 500, 558
- **Post-exercise**: 381, 398, 434, 562, 496, 485, 446, 479, 422

**Example Exercise:**

An investigation is conducted to determine whether there is a significant change in body temperature due to exercise. The pre-exercise and post-exercise body temperatures are gathered for eight individuals to perform a paired t-test analysis.

**Instructions:**

1. Calculate the difference in temperatures for each individual before and after exercise.
2. Use the differences to find the mean and standard deviation.
3. Formulate the null and alternative hypotheses.
   - Null hypothesis (H0): There is no difference in mean body temperature before and after exercise.
   - Alternative hypothesis (H1): There is a difference in mean body temperature before and after exercise.
4. Compute the test statistic and compare it with the critical value to determine if the null hypothesis can be rejected.
Transcribed Image Text:**The Paired t-Test** The following data are for pre-exercise and post-exercise body temperature measurements for eight young adults. Is there a difference in mean body temperature following exercise? - **Individual Number**: 1, 2, 3, 4, 5, 6, 7, 8 - **Resting**: 994, 291, 360, 385, 500, 558 - **Post-exercise**: 381, 398, 434, 562, 496, 485, 446, 479, 422 **Example Exercise:** An investigation is conducted to determine whether there is a significant change in body temperature due to exercise. The pre-exercise and post-exercise body temperatures are gathered for eight individuals to perform a paired t-test analysis. **Instructions:** 1. Calculate the difference in temperatures for each individual before and after exercise. 2. Use the differences to find the mean and standard deviation. 3. Formulate the null and alternative hypotheses. - Null hypothesis (H0): There is no difference in mean body temperature before and after exercise. - Alternative hypothesis (H1): There is a difference in mean body temperature before and after exercise. 4. Compute the test statistic and compare it with the critical value to determine if the null hypothesis can be rejected.
Expert Solution
Step 1

Given:

346
496
352
378
315
420
485
446
479
422
494
289
436
516
615
491
360
385
500
558
381
303
434
562
496

Hypothesized mean μ=425

Assumed significance level = 0.05

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