Answer :
Final Answer:
A chemical process converts lead to gold. It is know that the process is normally distributed. Suppose that a sample of n=15 observations were collected, and the sample mean is 99.8 and sample standard deviation is 2.0. No, we cannot conclude that μ=100 g given α=0.05.
Explanation:
Hypothesis testing is a statistical method used to determine if a sample provides enough evidence to make a claim about a population parameter. In this case, the null hypothesis (H0) is that μ (population mean) equals 100 g, while the alternative hypothesis (H1) is that μ does not equal 100 g.
To test this, we perform a one-sample t-test. With a sample size (n) of 15, a sample mean of 99.8, and a sample standard deviation of 2.0, we calculate the t-statistic:
t = (99.8 - 100) / (2.0 / √15) ≈ -0.447
Using a significance level (α) of 0.05, and with 14 degrees of freedom (n-1), the critical t-value for a two-tailed test is approximately ±2.145.
Since our calculated t-statistic (-0.447) falls within the range of -2.145 to 2.145, we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that μ is different from 100 g at the 0.05 significance level. In other words, we cannot say with confidence that the chemical process does not convert lead to gold with a mean of 100 g based on this sample data.
Learn more about Hypothesis testing
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