The Momoland Springs Company claims that there are at most 1 ppm (parts per million) of benzene in their water. Test at a=.10

n=25
= 1.10 ppm
s = .20 ppm

To determine whether the Momoland Springs Company's claim of having at most 1 ppm of benzene in their water is true or not, we can conduct a hypothesis test. Let's define our null and alternative hypotheses:

Null Hypothesis (H0): The true mean benzene level in the water is equal to 1 ppm.
Alternative Hypothesis (Ha): The true mean benzene level in the water is greater than 1 ppm.

To conduct this hypothesis test, we need to use the given information, which includes the sample size (n), sample mean (x̄), and sample standard deviation (s).

n = 25 (sample size)
x̄ = 1.10 ppm (sample mean)
s = 0.20 ppm (sample standard deviation)

Since the population standard deviation (σ) is not provided, we'll use the t-distribution for this hypothesis test.

The first step is to calculate the test statistic, which in this case is the t-value. The formula to calculate the t-value is given by:

t = (x̄ - μ) / (s / √n)

Where:
x̄ is the sample mean
μ is the population mean
s is the sample standard deviation
n is the sample size

In this case, the population mean (μ) is the hypothesized value of 1 ppm.

Next, we calculate the t-value using the given information:

t = (1.10 - 1) / (0.20 / √25)
t = 0.10 / (0.20 / 5)
t = 0.10 / 0.04 = 2.5

Now, we need to find the p-value associated with this t-value. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

To find the p-value, we can refer to a t-distribution table or use statistical software.

Based on the given significance level (α = 0.10), we want to compare the p-value to α to determine whether we reject or fail to reject the null hypothesis.

If the p-value is less than α (p < α), we reject the null hypothesis. However, if the p-value is greater than or equal to α (p ≥ α), we fail to reject the null hypothesis.

Once you obtain the p-value, compare it to the significance level α to make the final decision. If the p-value is less than 0.10, you can reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the true mean benzene level in the water is greater than 1 ppm.