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statistics
elementary statistics in social research

Questions and Answers of Elementary Statistics In Social Research

A sporting goods manufacturer claims that the variance of the strengths of a certain fishing line is 15.9. A random sample of 15 fishing line spools has a variance of 21.8. At α = 0.05, is there
Claim: σ2 ≤ 17.6; α = 0.01. Sample statistics: s2 = 28.33, n = 41 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population
Claim: σ2 > 19; α = 0.1. Sample statistics: s2 = 28, n = 17 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is
Claim: σ2 ≠ 32.8; α = 0.1. Sample statistics: s2 = 40.9, n = 101 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population
Claim: σ2 = 63; α = 0.01. Sample statistics: s2 = 58, n = 29 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is
A helmet manufacturer claims that the variance of the thickness in a helmet model is 7.5. A random sample of 15 helmets has a variance of 2.7. At α = 0.10, is there enough evidence to reject the
A library claims that the standard deviation of the reading days for readers of a particular book is no more than 2 days. A random sample of 30 readers has a standard deviation of 3 days. At α =
\(\mu \leq 100\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\mu eq 48\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(p
\(\mu=16\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\sigma>2.5\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(p \leq 0.4\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
A car rental company claims that its cars are driven for at least 10,000 miles on an average.(a) state the null and alternative hypotheses and identify which represents the claim, (b) describe type I
A soft drink manufacturing company claims that the mean number of milligrams of sodium in one serving is less than 25.(a) state the null and alternative hypotheses and identify which represents the
Left-tailed test, \(z=-1.18, \alpha=0.05\)Find the P-value for the hypothesis test with the standardized test statistic \(z\). Decide whether to reject \(H_{0}\) for the level of significance
Two-tailed test, \(z=2.57, \alpha=0.10\)Find the P-value for the hypothesis test with the standardized test statistic \(z\). Decide whether to reject \(H_{0}\) for the level of significance
Claim: \(\mathrm{H}_{0}: \mu=3725 ; \alpha=0.10 ; \sigma=121\). Sample statistics: \(\bar{x}=3748, n=30\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\).
Claim: \(\mu
Claim: \(\mu eq 21.25 ; \alpha=0.03 ; \sigma=4.35\). Sample statistics: \(\bar{x}=19.7, n=60\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the
Claim: \(\mu=930 ; \alpha=0.10 ; \sigma=30\). Sample statistics: \(\bar{x}=937, n=30\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population
Two-tailed test, \(\alpha=0.05, n=18\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Left-tailed test, \(\alpha=0.025, n=39\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Right-tailed test, \(\alpha=0.05, n=12\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Two-tailed test, \(\alpha=0.01, n=20\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Claim: \(\mu
Claim: \(\mu=195 ; \alpha=0.10\). Sample statistics: \(\bar{x}=190, s=36, n=101\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is
Claim: \(\mu eq 3,330,000 ; \alpha=0.05\). Sample statistics: \(\bar{x}=3,293,995, s=12,801, n=35\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the
Claim: \(p
Right-tailed test, \(n=20, \alpha=0.05\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Two-tailed test, \(n=14, \alpha=0.01\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Two-tailed test, \(n=41, \alpha=0.10\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Left-tailed test, \(n=6, \alpha=0.05\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At α = 0.01, can you reject the company’s claim? Assume the population
A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, Washington, is more than \($36.\) You want to test this claim. In a random sample of
A government agency reports that the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is $47,254.In a random sample of 15 full-time workers ages
A weight loss program claims that program participants have a mean weight loss of at least 10.5 pounds after 1 month. The weight losses after 1 month (in pounds) of a random sample of 40 program
A nonprofit consumer organization says that less than 18% of the vehicles the organization rated in a recent year have an overall score of 78 or more.In a random sample of 90 vehicles the
In Exercise 5, the nonprofit consumer organization says that the standard deviation of the vehicle rating scores is 11.90. A random sample of 90 vehicle rating scores has a standard deviation of
Classify each pair of samples as independent or dependent.1. Sample 1: Triglyceride levels of 70 patients Sample 2: Triglyceride levels of the same 70 patients after using a triglyceride-lowering
A credit card watchdog group claims that there is a difference in the mean credit card debts of people in California and Florida. The results of a random survey of 250 people from each state are
A travel agency claims that the average daily cost of meals and lodging for vacationing in Texas is less than the average daily cost in Virginia. The table at the left shows the results of a random
A non-governmental organization wants to choose between two regions in a state to initiate a campaign for rainwater harvesting. A researcher claims that Region A receives lesser rainfall than Region
The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown at the left. Can you conclude that there is a difference in the
A manufacturer claims that the mean driving cost per mile of its sedans is less than that of its leading competitor. You conduct a study using 30 randomly selected sedans from the manufacturer and 32
A channel claims that the mean amount of money spent by a family at movie theaters is greater than the mean amount spent by a family at amusement parks. The results for samples of expenses for the
A manager claims that the defects in units produced at Site A are more than the defects in units produced at Site B. The sample of 23 units from Site A contain a mean of 78 defects and a standard
In a study published in the Journal of the American Medical Association, three groups of 18 - to 35 -year-old participants overate for an 8 -week period. The groups consumed different levels of
A shoe manufacturer claims that athletes can increase their vertical jump heights using the manufacturer's training shoes. The vertical jump heights of eight randomly selected athletes are measured.
The campaign staff for a state legislator wants to determine whether the legislator's performance rating \((0-100)\) has changed from last year to this year. The table below shows the legislator's
A cookie manufacturer claims that its new cookies have more fiber than the ones produced by its competitor. The table shows the fiber content in seven samples of each type of cookies produced by the
In a derby, eight jockeys are riding a few exceptionally well-trained horses. As part of the race, the horses are timed as they run an obstacle course. The table shows the times (in seconds) of the
The standard deviation of the sale price of a bike is no more than $225.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A museum claims that its mean daily attendance is at least 300 people.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A microwave manufacturer claims that the mean life of the thermostat for a certain model of microwave is more than 4 years.Write the claim as a mathematical statement. State the null and alternative
As stated by a courier company’s dispatch department, the number of delivery errors per million consignments has a standard deviation that is less than 2.Write the claim as a mathematical
An online food delivery website claims that at least 75% of its new customers will return to place their next order.Describe type I and type II errors for a hypothesis test of the indicated claim.
A hose manufacturer claims that the maximum water flow rate in a garden is 40 liters per minute.Describe type I and type II errors for a hypothesis test of the indicated claim.
A local cricket club claims that the length of time to bowl an over has a standard deviation of more than 4 minutes.Describe type I and type II errors for a hypothesis test of the indicated claim.
A researcher claims that the percentage of adults in Egypt who own a surround sound speaker is not 40%.Describe type I and type II errors for a hypothesis test of the indicated claim.
A data encryption company publicizes that at least 98% of the systems using their software are protected.Describe type I and type II errors for a hypothesis test of the indicated claim.
A laptop repair shop advertises that the mean cost of repairing a laptop is less than $125.Describe type I and type II errors for a hypothesis test of the indicated claim.
A glass manufacturer claims that the mean number of glasses that break is no more than 3 glasses per production run.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test
An insurance agent claims that at least 65% of all businesses have a fire insurance policy.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed,
An IT college claims that its mean placement rate is 95%.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your
A derby analyst claims that the standard deviation of a jockey clearing the obstacles is less than 2 obstacles.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is
A polling organization reports that the number of samples distributed to 5,000 households does not increase the mean sale by 5,000 units.State H0 and Ha in words and in symbols. Then determine
A researcher claims that standard deviation of the life span of a brand of air conditioner is at most 4.6 years.Determine whether the claim represents the null hypothesis or the alternative
A scientist claims that the mean number of migratory bird species is less than 3,800.Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is
An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 5.6 kilometers per liter.Determine whether the claim represents the null
A non-governmental organization claims that none of the children in a particular slum area get a balanced diet. Determine whether the claim represents the null hypothesis or the alternative
A fitness research team is investigating the mean cost of a 45-day weight loss course. A fitness center thinks that the mean cost is less than $75. You want to support this claim. How would you write
An internet service provider claims that the mean bandwidth drop time is about 7 minutes. You work for one of the ISP’s competitors and want to reject the claim. How would you write the null and
A carbine manufacturer claims that the mean life span of its competitor’s carbines is less than 46 runs.You are asked to perform a hypothesis test to test this claim. How would you write the null
The P-value for a hypothesis test is P = 0.0237. What is your decision when the level of significance is (1) α = 0.05 and (2) α = 0.01?
Find the P-value for a left-tailed hypothesis test with a standardized test statistic of z = –2.23. Decide whether to reject H0 when the level of significance is α = 0.01.
Find the P-value for a two-tailed hypothesis test with a standardized test statistic of z = 2.14. Decide whether to reject H0 when the level of significance is α = 0.05.
In auto racing, a pit stop is where a racing vehicle stops for new tires, fuel, repairs, and other mechanical adjustments. The efficiency of a pit crew that makes these adjustments can affect the
According to a study of U.S. homes that use heating equipment, the mean indoor temperature at night during winter is 68.3°F. You think this information is incorrect. You randomly select 25 U.S.
Use the TI-84 Plus displays to make a decision to reject or fail to reject the null hypothesis at a level of significance of α = 0.05. TI-84 PLUS Z-Test Inpt: Data Stats Ho:6.2 :.47 x:6.07 n:53 Po
Find the critical value and rejection region for a left-tailed test with α = 0.01.
Find the critical values and rejection regions for a two-tailed test with α = 0.05.
Employees at a construction and mining company claim that the mean salary of the company’s mechanical engineers is less than that of one of its competitors, which is \($88,200.\) A random sample of
A researcher claims that the mean annual cost of raising a child (age 2 and under) by married-couple families in the U.S. is \($14,050.\) In a random sample of married-couple families in the U.S.,
Explain the difference between the z-test for μ using a P-value and the z-test for μ using rejection region(s).
A manufacturer of smoke detectors designed for fire protection claims that the average area that the smoke detector covers is at least 60 square meters. To test this claim, you randomly select a
A cookie manufacturer claims that the mean sugar content in each of the cookies produced is no more than 18%. A random sample of 56 cookies has a mean sugar content of 19%. Assume the population
An LED lamp manufacturer guarantees that the mean life of a certain type of LED lamp is at least 25,000 hours. A random sample of 49 LED lamps has a mean life of 24,800 hours. Assume the population
Find the critical value t0 for a left-tailed test with α = 0.05 and n = 21.
Find the critical value t0 for a right-tailed test with α = 0.01 and n = 17.
Find the critical values –t0 and t0 for a two-tailed test with α = 0.10 and n = 26.
A used car dealer says that the mean price of used cars sold in the last 12 months is at least \($21,000.\) You suspect this claim is incorrect and find that a random sample of 14 used cars sold in
An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 39 water samples and measure the pH of each.The sample mean and standard deviation are
A department of motor vehicles office claims that the mean wait time is less than 14 minutes. A random sample of 10 people has a mean wait time of 13 minutes with a standard deviation of 3.5 minutes.
An estate agent says that the mean rental of a warehouse (with basic amenities) is \($2,500.\) You suspect this claim is incorrect and find that a random sample of 38 such warehouses has a mean
A call center claims that the mean wait time for a customer to connect with a customer care executive is at most 2.5 minutes. A random sample of 35 calls at the call center has a mean wait time of
Flash Drive Cycles A company claims that the mean number of usage cycles of their flash drives is at least 25,000 hours. You suspect this claim is incorrect and find that a random sample of 15 flash
You receive a brochure from a courier company. The brochure indicates that the mean number of deliveries per deliveryman is more than 28 packets per day. You want to test this claim. You randomly
The director of a courier company estimates that the mean time spent by a deliveryman in dropping off packages per day is 6.0 hours. As a member of the labor union, you want to test this claim. A
In an article in the Journal of Statistics Education (vol. 4, no. 2), Allen Shoemaker describes a study that was reported in the Journal of the American Medical Association (JAMA).* It is generally

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