Question

Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that the unsafe amount of perchlorate is present in their drinking water. Drinking water is safe when the perchlorate level is 24.5 parts per billion (ppb) or smaller. Suppose we sampled 28 water sources in the area (former rocket-testing site), and found an average amount of perchlorate 25.3 ppb and standard deviation 4.5 ppb. Conduct a test, at a 5% significance level, to determine if the water in this area is unsafe to drink. (a) (1pt) State the hypotheses. (b) (3pts) Calculate the test statistic. (c) (2pts) Calculate the p-value. Note: Be sure to give your RStudio code in your answer. (d) (2pts) What do the data suggest? Select one. A) The data provide convincing evidence that the drinking water in the area is unsafe to drink. B) The data show insufficient evidence that the drinking water in the area is unsafe to drink. 

          Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that the unsafe amount of perchlorate is present in their drinking water. Drinking water is safe when the perchlorate level is 24.5 parts per billion (ppb) or smaller. Suppose we sampled 28 water sources in the area (former rocket-testing site), and found an average amount of perchlorate 25.3 ppb and standard deviation 4.5 ppb. Conduct a test, at a 5% significance level, to determine if the water in this area is unsafe to drink.

(a) (1pt) State the hypotheses.

(b) (3pts) Calculate the test statistic.

(c) (2pts) Calculate the p-value. Note: Be sure to give your RStudio code in your answer.

(d) (2pts) What do the data suggest? Select one.

A) The data provide convincing evidence that the drinking water in the area is unsafe to drink.
B) The data show insufficient evidence that the drinking water in the area is unsafe to drink.
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Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that the unsafe amount of perchlorate is present in their drinking water. Drinking water is safe when the perchlorate level is 24.5 parts per billion (ppb) or smaller. Suppose we sampled 28 water sources in the area (former rocket-testing site), and found an average amount of perchlorate 25.3 ppb and standard deviation 4.5 ppb. Conduct a test, at a 5% significance level, to determine if the water in this area is unsafe to drink. (a) (1pt) State the hypotheses. (b) (3pts) Calculate the test statistic. (c) (2pts) Calculate the p-value. Note: Be sure to give your RStudio code in your answer. (d) (2pts) What do the data suggest? Select one. A) The data provide convincing evidence that the drinking water in the area is unsafe to drink. B) The data show insufficient evidence that the drinking water in the area is unsafe to drink.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that the unsafe amount of perchlorate is present in their drinking water. Drinking water is safe when the perchlorate level is 24.5 parts per billion (ppb) or smaller. Suppose we sampled 28 water sources in the area (former rocket-testing site), and found an average amount of perchlorate 25.3 ppb and standard deviation 4.5 ppb. Conduct a test, at a 5% significance level, to determine if the water in this area is unsafe to drink. (a) (1pt) State the hypotheses. (b) (3pts) Calculate the test statistic. (c) (2pts) Calculate the p-value. Note: Be sure to give your RStudio code in your answer. (d) (2pts) What do the data suggest? Select one. A) The data provide convincing evidence that the drinking water in the area is unsafe to drink. B) The data show insufficient evidence that the drinking water in the area is unsafe to drink.
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Transcript

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00:01 It's stated in this question that drinking water is safe when the preclarate levels are 24 .5 parts per billion or less.
00:10 And so we want to test if this level is exceeded in some water.
00:15 We are asked to test at a significant level of 5 percent.
00:19 And to do so, we sampled 28 water sources and found that among these 28, there was a sample mean of 25 .3 parts per billion, and a sample standard deviation of four and a half parts per billion.
00:35 For part a, we are asked to state the hypotheses.
00:39 Now, the null hypothesis here would be that there is no problem, that the mean concentration is 24 .5 parts per billion.
00:50 And the alternative hypothesis is that the mean exceeds the safe level.
00:58 For b, we're asked to calculate the test statistic.
01:01 Now, since we do not know the population standard deviation, we are relying on on using the sample standard deviation.
01:08 And in this case, the test statistic is based on the t distribution with n minus 1 or 27 degrees of freedom.
01:16 Test statistic is calculated as the sample mean minus the null hypothesized mean divided by the sample standard deviation over the square root of the sample size.
01:43 And this comes out to approximately 0 .9407 for c - where it has to calculate a p -value from the test statistic.
01:58 So since this is a right -tailed test, we know that by looking at the alternative hypothesis, it's a greater than hypothesis.
02:06 The p -value is equal to the probability of having gotten a test statistic, at least as great as the one that we got.
02:16 And keep in mind that this is the t distribution based on 27 degrees of freedom...
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