Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 13 22 13 13 7 12 23 19 11 9 13 4 The sample mean is x = 12.4%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance?  State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?  H0: μ ≠ 11%; H1: μ = 11%; two-tailedH0: μ = 11%; H1: μ ≠ 11%; two-tailed    H0: μ = 11%; H1: μ < 11%; left-tailedH0: μ = 11%; H1: μ > 11%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.  The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.  The standard normal, since we assume that x has a normal distribution with unknown σ. The Student's t, since we assume that x has a normal distribution with known σ. Compute the z value of the sample test statistic. (Round your answer to two decimal places.)  (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)  (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) State your conclusion in the context of the application.  There is sufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average. There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.

Question

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.

16 6 8 9 13 22 13 13
7 12 23 19 11 9 13 4

The sample mean is x = 12.4%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01.

(a) What is the level of significance? 
 

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? 
H0: μ ≠ 11%; H1: μ = 11%; two-tailedH0: μ = 11%; H1: μ ≠ 11%; two-tailed    H0: μ = 11%; H1: μ < 11%; left-tailedH0: μ = 11%; H1: μ > 11%; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 
The Student's t, since n is large with unknown σ.
The standard normal, since we assume that x has a normal distribution with known σ.
 The standard normal, since we assume that x has a normal distribution with unknown σ.
The Student's t, since we assume that x has a normal distribution with known σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 
 

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 
 


(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) State your conclusion in the context of the application. 
There is sufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.
There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.    

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Other

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: The data 17.7 33.5 26.3 22.9 21.4 e 28.9 24.2 18.3 27.9 21.2 19.2 22.121.6 37.7 37.4 presents the bo...

A: Frequency distribution:Frequency of an interval is the number observations that fall in that interva...

Q: I need help with understanding standard deviation.  How to calculate it from the mean?

A: The standard deviation describes the spread of the data distribution from the mean of the given data...

Q: What’s the mean annual return of the S&amp;P 400 Midcap Index over the past 7 years?  What’s the sta...

A: Hello there! there are more than three sub parts in the given question. According to our policies we...

Q: A, B, C

A: In this question we have given a data of 10 sample observation based on that data we have to find co...

Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of who...

A: (A)The sample mean and standard deviation is calculated below:

Q: Find the standard deviation, s, of sample data summarized in the frequency distribution table given ...

A: Using the provided formula, the sample standard deviation of the provided frequency distribution is ...

Q: Hi. I need help with part (c) only. Consider the accompanying 2 × 3 table displaying the sample prop...

A: Let us assume the total sample size be n. Writing the given proportions as number of people we get a...

Q: In a recent court case it was found that during a period of 11 years 851 people were selected for gr...

A: It is given that a particular ethnicity in the population is 40%. From that ethnicity, 80% of 851 pe...

Q: If 25% of U.S. federal prison inmates are not U.S. citizens, find the probablity that 2 randomly sel...

A: Hello there! There are more than one question in the file shared. According to our policies cannot a...

Q: A researcher says that 50% of the variance in blood pressure can be predicted from HR and that blood...

A: In this question we have the value of coefficient of determination which is equal to 0.50 and we hav...

Q: Number 15 A B C D

A: Note:Thank you for the question. However, your question has more than 3 parts. We are solving first ...

Q: Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the...

A: In this question, there is total 32 songs collection out of which 11 songs by Frank Sinatra, 13 song...

Q: you gave me this answer in last question, (copied below) but I see why I wasn't finding the correct ...

A: Note:Thank you for letting us know your doubt. We shall try our best to help you understand clearly ...

Q: The Orchard Cafe has found that about 10% of the diners who make reservations don't show up. If 86 r...

A: Binomial distribution:A random variable X follows binomial distribution if it follows the given prop...

Q: Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). T...

A: Confidence interval when population standard deviation is not known:The formula of confidence interv...

Q: A personnel director in a particular state claims that the mean annual income is the same in one of ...

A: According to the given question, in order to test that the annual income is the same in one of the​ ...

Q: You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, ...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: Suppose x has a distribution with μ = 60 and σ = 17. (a) If random samples of size n = 16 are select...

A: Note:Hi there! Thank you for posting the question. The Part (b) of your question asks about the “x d...

Q: How do I solve this question with this table? obtain this sample using the portion of the random num...

A: By using random number table we can determine the random sampling with equal chance of occurrences o...

Q: Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organ...

A: Let X be the random variable, defined as the oxygen demand.Here, X follows normal distribution with ...

Q: See attachment for question.

A: Given X(n,p) is a binomial random variable with parameters n,p.n is total number of trailsp is proba...

Q: please answer the whole question  (3) Let x be per capita income in thousands of dollars. Let y be t...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Q: Doctor Frederick believes the population mean weight of adult male patients in his practice is exact...

A: The aim is to find the accurate statement from the following options to evaluate the claim that the ...

Q: Find the​ mean, median, and mode of the​ data, if possible. If any of these measures cannot be found...

A: The sample data of seven admission test scores for a professional school is provided.Here, n = 7.The...

Q: A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7...

A: The provided information are:

Q: For mode of Beta Distribution with parameters Alpha and Beta, why are the bounds when alpha and beta...

A: Beta FunctionIt is an area function and defined by a definite integral 

Q: This study investigated the cognitive effects of stimulant medication in children with Attention-Def...

A: Solution:The appropriate statistical analysis to determine if there is an effect of drug dose on CPT...

Q: According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shape...

A: Chebyshev’s inequality:Chebyshev’s rule is appropriate for any distribution. That is, Chebyshev’s in...

Q: If the probability for an event E is P(E)=0.4, then what are the odds against E?

A: Odds against an event:The odds against an event is given by the ratio of the probability of the even...

Q: A, B, C

A: a.The two populations are ‘all the students who purchase lecture notes’ and ‘all the students who do...

Q: Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, am...

A: Test statistic calculation:The test hypotheses are:Null hypothesis:H0: p = 0.03, that is, 3% in the ...

Q: A student takes a multiple-choice test that has 20 questions. Each question has five choices. The st...

A: Binomial distribution:It is a discrete probability distribution in which each trials have exactly tw...

Q: Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company c...

A: State the appropriate hypothesis:Let p be the population proportion of blue candies.A candy company ...

Q: a. Which of the six correlations above are statistically significant (i) if you test each correlatio...

A: We have been given alpha  = 0.05 which implies that the probability of inferring that there is a cor...

Q: The same media consultants decided to continue their investigation of the focal relationship between...

A: In this question, the statistical summary about three models represented by three equation has given...

Q: A. A population has a mean of 6.9 and standard deviation of 2.6. Find the value that has 80% of the ...

A: Given Population mean = 6.9Standard deviation = 2.6The Z score with the area left to it close to 0.8...

Q: If a chicken and a half lays an egg and a half in a day and a half how many eggs can 30 chickens lay...

A: It is given that a chicken and a half lays an egg and a half, in a day and half.That is, 1.5 chicken...

Q: 1. In a random sample of 15 CD players brought in form repair, the average repair cost was $80 and t...

A: It is given that the average repair cost (mean) is $80, sample standard deviation s is $14, the samp...

Q: Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of ...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Q: Suppose x has a distribution with μ = 60 and σ = 17. (a) If random samples of size n = 16 are select...

A: Note:Hi there! Thank you for posting the question. The Part (b) of your question asks about the “x d...

Q: A group of data items and their mean are given. 12, 20, 28, 48, 72, 108;  Mean=48 A. Type the deviat...

A: A.Computing the deviation from mean for each of the data:Here the data items are 12, 20, 28, 48, 72,...

Q: Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? ...

A: (a) Scatter diagram of the data:The line that best fits the data is least-squares regression line.Th...

Q: About 42.3% of Californians and 19.6% of all Americans over age five speak a language other than Eng...

A: Solution:Let us consider that your class has 30 students.Null and alternative hypotheses:Here, to ch...

Q: Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? ...

A: Part (a):The scatter diagram, along with the best fitted line (least-squares regression line) for th...

Q: Consider a drug testing company that provides a test for marijuana usage. Among 301 tested subjects,...

A: Given hypothesis testp be the proportion of wrong test results Null hypothesis : p = 0.10Alternate H...

Q: A sample of 50 women is​ obtained, and their heights​ (in inches) and pulse rates​ (in beats per​ mi...

A: According to the provided data, the variable x represents the height of the women. The sample size, ...

Q: In Spetember of 2013, Mario The Baker introduced a new chocolate cake and hired Doug and Jeremy to b...

A: Description of events A and B:It is given that 40% of the cakes got “thumbs up” out of 70% of the ca...

Q: Please answer the attached picture. Thanks,

A: Г(1,Ɵ) represents a gamma distribution X~ Г(α,λ) where α is the shape parameter and λ is the scale p...

Q: Students were​ asked, "How stressed have you been in the last​ week, on a scale of 0 to​ 10, with 0 ...

A: Histogram:Histogram is a bar graph that represents a frequency distribution.

Q: Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as ...

A: Hello there! there are moe than three subparts in the question. According to our policies cannot ans...