Statistical Inference Calculator

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Example

Created on 2024-06-20Asked by Lucas King (Solvelet student)

Perform a hypothesis test for the mean with the following data: sample mean

\bar{x} = 20

, population mean

\mu = 18

, standard deviation

\sigma = 4

, and sample size

n = 30

Solution

To perform a hypothesis test for the mean with the given data: 1. **State the null and alternative hypotheses:**

H_0: \mu = 18

H_a: \mu \neq 18

2. **Calculate the test statistic:**

z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} = \frac{20 - 18}{4 / \sqrt{30}} = \frac{2}{0.73} \approx 2.74.

3. **Find the p-value:** Using standard normal distribution tables,

P(Z > 2.74) \approx 0.0031

. 4. **Conclusion:** Since the p-value is less than 0.05, we reject the null hypothesis. There is significant evidence to suggest that the population mean is different from 18. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Mia Campbell on Solvelet

1. Conduct a hypothesis test to determine if the mean weight of a sample of apples is different from 150 grams, given a sample mean of 155 grams and a sample standard deviation of 10 grams.2. Use a confidence interval to estimate the population proportion of individuals who prefer a certain brand of soda.,

DefinitionStatistical inference is the process of deducing characteristics of an underlying distribution using data. And it has everything you need to know about hypothesis testing, estimation, and confidence intervals. We may estimate the population mean by the sample mean and output a 95% confidence interval as an indication of a range within which the population mean likely lies.

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