For each of the following assertions, state whether it is a legitimate statistical hypothesis and why:a. $\quad H: \sigma>100$b. $H: \tilde{x}=45$c. $H: s \leq 20$d. $H: \sigma_{1} / \sigma_{2}<1$e. $H: \bar{X}-\bar{Y}=5$f. $H: \lambda \leq 01,$ where $\lambda$ is the parameter of an exponential distribution used to model component lifetime
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Given Data: Let 'X' represent the amount of nicotine X~ Normal (0.888, 0.3112) n=30 Therefore, X¯~…
Q: The weight in tons of the iron stone lled in a railcar is a random variable with expectation 8 and…
A:
Q: A medical research team claims that the mean recovery time for patients after the new surgical…
A: here use basic of hypothesis test
Q: A company that manufactures batteries used in electric cars is reporting that their newest model of…
A: Given information Sample mean x̅ = 13.1 Population mean µ = 12 Sample size = 35 Standard deviation σ…
Q: A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed…
A:
Q: Given a normally distributed population with a mean of -55 and standard deviation of 20, what is the…
A: Let x¯ be the mean of a random sample which follows normal distribution. The sample size is 20, mean…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A:
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: The probability of randomly selecting 31 cigarettes with a mean of 0.897 g or less is, The…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: P(X<0.877)=PX<0.877-0.9260.28147=P(Z<-0.0490.040988)=P(z<-1.20)=0.1159~0.116
Q: The television picture tubes of manufacturer Sumsun have a mean lifetime of 7 years and a standard…
A: In statistical hypothesis, there are two kinds of sample tests. Small sample test and large sample…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: We have to find probabaility.
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A:
Q: A company that manufactures batteries used in electric cars is reporting that their newest model of…
A:
Q: he amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.939…
A: From the given information, The amounts of nicotine in a certain brand of cigarette are normally…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Given information: The amounts of nicotine (X) in a certain brand of cigarette are normally…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Here, µ = 0.907, σ = 0.293, and n = 35.
Q: nt of time a random sample of 47Americans 16 and older spent watching television each day is 3.1…
A: As the population standard deviation is known, we will use z distribution. The 90% confidence for…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Concept of sampling distribution of sample mean: Let a particular characteristic of a population is…
Q: Two machines used to fill soft drink containers are being compared. The number of containers filled…
A: Solution : Given : n1=n2 = 60 x¯1 = 74.5 s1 = 6.9 x¯2 = 75…
Q: Engr. Vasquez and his group of IE students shall test the compressive strength of material X. In…
A: Answer: None of the above. The probability that X falls between 2995 psi to 3010 psi is 0.07962.…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A:
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A:
Q: The number of supermarkets in the City of East Tampa follows a Poisson process with the mean number…
A: Probability distribution
Q: An investment adviser advertises that their clients have, on average, earned at least $260 profit on…
A:
Q: We have just conducted a study comparing cognitive development of low- and normal-birthweight babies…
A: The hypotheses are given below: Null hypothesis: H0: µ1 = µ2 Alternative hypothesis: HA: µ1 ≠ µ2…
Q: It is believed that the average height of General Engineering (GE) students is 1.72 meters, which is…
A: Given: x¯1=1.75σ1=0.34n1=49x¯2=1.66σ2=0.3n2=36 Level of significance=α=5%=0.05
Q: The supervisor of a dairy milk chocolate factory has observed that the weight of each 32g chocolate…
A: From the provided information, Mean (µ) = 32.2 g Standard deviation (σ) = 0.3g X~N (32.2, 0.3) Here…
Q: A state Department of Transportation claims that the mean wait time for various services at its…
A: Given dataµ = 6Sample size = 16s = 7.3x̅ = 9.5Significance level (α) = 0.01Formulation of Hypothesis
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: The probability of randomly selecting 49 cigarettes with mean of 0.886 g or less is obtained below:…
Q: According to the records of an electric company serving the Boston area, the mean electricity…
A: Given data,μ=1650σ=320P(X<1903)=?
Q: The number of supermarkets in the City of East Tampa follows a Poisson process with the mean number…
A: Discrete Probability distribution
Q: ertain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year.…
A: a) x~N(3,0.25)
Q: It is known that the standard deviation of the marks of a certain Mathematics exam is 2.4. For a…
A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…
Q: uppose that the talk time on a fully charged iPhone is approximately normally distributed with mean…
A:
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: As given the amounts of nicotine in a certain brand of cigarettes are normally distributed with a…
Q: Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have…
A: The hypothesis test is a statistical method in which one using the sample data try to check the…
Q: A hospital administrator finds that the mean hospital stay for a sample of 77 women after childbirth…
A: The sample mean is x=3.1 days The population mean is μ=2.7 days. The null and alternative hypothesis…
Q: Suppose that the talk time on a fully charged iPhone is approximately normally distributed with mean…
A: Mean, µ=7; Standard deviation, σ=0.8.
Q: The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries…
A: Step 1 Solution: State the hypotheses. Null hypothesis: H0: µ≥45 That is, the mean life of…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Given information Mean (µ) = 0.935 g Standard Deviation(σ) = 0.283 g Sample size (n)= 41
Q: The time required to install a new jeepney engine is normally distributed random variable with a…
A: (1) Let X denote the time required to install a new jeepney engine and it follows normal…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: We have to find probability using z table.
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A:
Q: If we have a sample of size 100 from a population of rope with sample mean breaking strength of 1040…
A: In this problem we have to see whether mean strength is greater than 1000 pounds and we will raise…
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: The probability of randomly selecting 38 cigarettes with a mean of 0.848 or less is 0.1587, which is…
Q: An automobile battery manufacturer company named Everlast conducted a test which indicates the…
A: Introduction: Define X as the random variable of interest here, which denotes the number of months…
Q: he amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.889…
A: The mean is 0.889 and the standard deviation is 0.324.
Q: A coin-operated soft-drink machine is designed to discharge, when it isoperating properly, at least…
A:
Q: The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of…
A: Given that, The amounts of nicotine in certain brand of cigarette are normally distributed with the…
Q: A cereal company claims that the mean weight of the cereal in itspackets is at least 14 oz.…
A: A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.…
For each of the following assertions, state whether it is a legitimate statistical hypothesis and why:
a. $\quad H: \sigma>100$
b. $H: \tilde{x}=45$
c. $H: s \leq 20$
d. $H: \sigma_{1} / \sigma_{2}<1$
e. $H: \bar{X}-\bar{Y}=5$
f. $H: \lambda \leq 01,$ where $\lambda$ is the parameter of an exponential distribution used to model component lifetime
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- Of a random sample of 100 college students, 35 expected to achieve a higher standard of living than their parents, 43 expected a lower standard of living, and 22 expected about the same standard of living as their parents. Do these data present strong evidence that, for the population of students, more expect a lower standard of living compared with their parents than expect a higher standard of living?It has been determined that 37 out of 100 adult Americans that did not attend college believe in extra-terrestrials. However, from a random sample of 100 adult Americans that did not attend college 43 claim that they believe in extra-terrestrials. Does this indicate that the proportion of people who did not attend college and who believe in extra-terrestrials has changed? Conduct a hypothesis test with a = 0.01 and interpret the results.Are college students more likely than high school students to have a part-time job? A recent study found that 21 out of a random sample of 51 college students had part-time jobs and that 12 out of a random sample of 40 high school students had part-time jobs. At the 5% level of significance, do these samples provide evidence that college students are more likely than high school students to have a part-time job? Be sure to clearly state the null and alternative hypothesis, calculate the test statistic and p-value, state the conclusion of the test, and interpret the result in context.
- A magazine reported that at the top 50 business schools in a region, students studied an average of 18.1 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 18.1 hour benchmark. State the null and alternative hypotheses.If we have a sample of size 100 from a population of rope with sample mean breaking strength of 1040 pounds with standard deviation 200 pounds and we wish to run a hypothesis test with this data to see if the population mean breaking strength exceeds 1000 pounds, what is our ALTERNATE HYPOTHESIS?In 1995, it was determined that 78% of US citizens supported a ban on household aerosols. Thinking that this proportion may have changed over the past few decades, a sample will be taken to test if a change has occurred. What is the appropriate null hypothesis? H0: ["", "", "", ""] What is the appropriate alternative hypothesis? Ha:
- The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: b. Based on the hypotheses, find the following: c. Test Statistic = d. p-value = e. Based on the above we choose to:_____________ f. The correct summary would be: ____________ that the true proportion of people in that city suffering from depression or a…The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? H0: H1: b.) Based on the hypotheses, find the following: c.) Test Statistic = d.) p-value = e.) Based on the above we choose to________________ f.) The correct summary would be:____________ that the true proportion of people in that city suffering from depression or a depressive illness is more than the percent in the general…One particular professional association of investors conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. The survey results showed 37.9% bullish, 22.6% neutral, and 39.5% bearish. Assume these results are based on a sample of 300 members. (a) Over the long term, the proportion of bullish members is 0.39. Conduct a hypothesis test at the 5% level of significance to see if the current sample results show that bullish sentiment differs from its long term average of 0.39. What are your findings? Formulate the hypotheses that can be used to determine whether the bullish sentiment differs from its long term average of 0.39. A. H0: p ≥ 0.39 Ha: p < 0.39 B. H0: p ≤ 0.39 Ha: p > 0.39 C. H0: p = 0.39 Ha: p ≠ 0.39 D. H0: p < 0.39 Ha: p ≥ 0.39 E. H0: p > 0.39 Ha: p ≤ 0.39 Find the value of the test…
- A consumer electronics firm has developed a new type of remote control button that is designed to operate longer before becoming intermittent. The best button on the market lasts an average of 1200 hours. A random sample of 36 new buttons is selected and each is tested in continuous operation until becoming intermittent. The resulting lifetime of each button was recorded and found to have a sample mean of 1275 hours. What is the appropriate null hypothesis? H0: ["", "", "", ""] What is the appropriate alternative hypothesis? Ha:A random sample of 104 marketing vice presidents from large Fortune 500 corporations was questioned on future developments in the business environment. Of those sample members, 50 indicated some measurement of agreement with this statement: Firms will concentrate their efforts more on cash flow than on profits. What is the lowest level of significance at which the null hypothesis, which states that the true proportion of all such executives who would agree with this statement is one-half, can be rejected against a two-sided alternative?Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 189 cases tested in a certain state, 12 were found to be drug-resistant. Suppose also that, of 429 cases tested in another state, 8 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state.) State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: ______ Ha: ______ Find the value of the test statistic. (Round your answer to two decimal places.) = What is the p-value? (Round your answer to four decimal places.) p-value =…