A market research company wishes to know how many energy drinks adults drink each week. They want to construct a confidence interval for
the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9 . The study found
that for a sample of 164 adults the mean number of energy drinks consumed per week is 7.9 . Construct the desired confidence interval. Round
your answers to one decimal place.
AnswerHow to enter your answer (opens in new window) 2 Points Keypad
Lower endpoint:

Question

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a

confidence interval for
the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9 . The study found
that for a sample of 164 adults the mean number of energy drinks consumed per week is 7.9 . Construct the desired confidence interval. Round
your answers to one decimal place.
AnswerHow to enter your answer (opens in new window) 2 Points Keypad
Lower endpoint:

UpStudy AI · Accepted Answer

To construct an 80% confidence interval for the mean number of energy drinks consumed per week, we'll use the following formula:

$$
\text{Confidence Interval} = \bar{x} \pm z_{\frac{\alpha}{2}} \times \left(\frac{\sigma}{\sqrt{n}}\right)
$$

Where:
- $$\bar{x} = 7.9$$ (sample mean)
- $$\sigma = 0.9$$ (population standard deviation)
- $$n = 164$$ (sample size)
- $$z_{\frac{\alpha}{2}}$$ is the z-score corresponding to the desired confidence level.

For an 80% confidence level, $$\alpha = 0.20$$, so $$\frac{\alpha}{2} = 0.10$$. The z-score corresponding to a cumulative probability of 0.90 is approximately $$1.28$$.

Now, calculate the margin of error:

$$
\text{Margin of Error} = 1.28 \times \left(\frac{0.9}{\sqrt{164}}\right) \approx 0.09
$$

Finally, construct the confidence interval:

$$
7.9 - 0.09 = 7.8 \quad \text{(Lower endpoint)}
$$
$$
7.9 + 0.09 = 8.0 \quad \text{(Upper endpoint)}
$$

**Answer:**  
Lower endpoint: 7.8

Upper endpoint: 8.0
Lower endpoint: 7.8

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Statistics Questions