Question

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0...

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 41 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 8 ppb; H1: μ < 8 ppb H0: μ = 8 ppb; H1: μ > 8 ppb H0: μ > 8 ppb; H1: μ = 8 ppb H0: μ < 8 ppb; H1: μ = 8 ppb H0: μ = 8 ppb; H1: μ ≠ 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and σ is known. The Student's t, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Homework Answers

Answer #1

(a) The level of significance is α = 0.01

The null and alternative hypothesis is ,

H0: μ = 8 ppb; H1: μ < 8 ppb

The test is left-tailed test.

(b) The Student's t, since the sample size is large and σ is unknown.

The test statistic is ,

(c) Now , df=degrees of freedom=n-1=41-1=40

The p-value is ,

p-value= ; The Excel function is , =TDIST(2.668,40,1)

From t-table , p-value <0.01

(d) Decision : Here , p-value < 0.01

Therefore , reject Ho.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

(e) There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0...
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well...
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0...
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well...
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0...
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well...
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average...
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.80 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01. (a) What is the level of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 with sample standard deviation s = 2.5. Use a...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.2. Use a...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.3. Use a...
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat...
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.0 inches. Do these data indicate that the average length of a trout caught in Pyramid...
Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report). A mean arsenic...
Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report). A mean arsenic level of 8 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crop. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of 7.2. Given that the standard deviation of arsenic level is 1.9, does this information indicate that the mean level of...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.5%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.2%. Do these data indicate that the dividend yield of all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT