The number of calories per candy bar for a random sample of standard-size candy bars is show below. Estimate the mean number of calories per candy bar with 98% confidence. Assume the population is normally distributed.
The number of calories per candy bar for a random sample of standard-size candy bars is show below. Estimate the mean number of calories per candy bar with 98% confidence. Assume the population is normally distributed.
The number of calories per candy bar for a random sample of standard-size candy bars is show below. Estimate the mean number of calories per candy bar with 98% confidence. Assume the population is normally distributed.
The number of calories per candy bar for a random sample of standard-size candy bars is show below. Estimate the mean number of calories per candy bar with 98% confidence. Assume the population is normally distributed.
Transcribed Image Text:The number of calories per candy bar for a random sample of standard-size candy bars is shown below. Estimate the mean number of calories per candy bar with 98% confidence. Assume the population is normally distributed.
Calories:
- 220
- 240
- 240
- 210
- 230
- 220
- 275
- 260
- 220
- 280
- 230
- 280
- 240
**Which formula will you use for this problem?**
Options:
1. \(\bar{x} - t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) < \mu < \bar{x} + t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right)\)
2. \(\bar{x} - z_{\alpha/2} \left(\frac{\sigma}{\sqrt{n}}\right) < \mu < \bar{x} + z_{\alpha/2} \left(\frac{\sigma}{\sqrt{n}}\right)\)
3. \(n = \left(\frac{z_{\alpha/2} \cdot \sigma}{E}\right)^2\)
4. \(n = \hat{p} \cdot \hat{q} \left(\frac{z_{\alpha/2}}{E}\right)^2\)
5. \(\hat{p} - z_{\alpha/2} \sqrt{\frac{\hat{p} \cdot \hat{q}}{n}} < p < \hat{p} + z_{\alpha/2} \sqrt{\frac{\hat{p} \cdot \hat{q}}{n}}\)
The selected formula is the first one, used for estimating the mean with confidence intervals, assuming a normally distributed population with a sample standard deviation.
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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