One Population Mean
Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. State the Null and the Alternate Hypothesis Statements
H0: M=4.5, H1: M>4.5
Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of teen girls smoke to stay thin? State the Null and Alternative Hypothesis.
H0: P=0.30
H1: P>0.30
The mean number of English courses taken in a two–year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Perform a hypothesis test at the 0.05 level to determine if there is a difference in the mean number of English courses taken by males is different than the mean number of English courses taken by females?
State H0,H1,p-val,Decision,Conclusion
1-Males 2-Females
H0:M1=M2
H1:M1/=M2
p-value: 0.0020
Reject the null.
There is enough evidence to conclude he mean number of English courses taken by males is different than the mean number of English courses taken by females.
A recent debate about where in the United States skiers believe the skiing is best prompted a survey. The results of the survey are found in Rguroo (Skiing) Test to see if the best ski area is independent of the level of the skier at the 0.05 significance level.
State the H0 and H1?
H0: Ski area and ski level are independent.
H1: Ski area and ski level are not independent.
An economist wondered if people who go to the movies on weekdays go more or less often on Fridays than any other day. She figured that if it were truly random, 20% of these movie-goers would go on Fridays. She randomly sampled 50 people who go to movies on weekdays and asked them on which day they attend movies most frequently. Of those sampled, 14 indicated that they go on Fridays more often than other days.
The economist conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of weekday movie-goers who go most frequently on Fridays is different from 20%.
State the H0, H1, p-value, Decision, Conclusion
H0:P=0.20
H1:P/=0.20
p-value: 0.1573
Fail to Reject the Null
There is not enough evidence to conclude the true proportion of weekday movie-goers who go most frequently on Fridays is different from 20%.
Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0.What is the p-value? Decision? Conclusion?
P value: 0.3179
Fail to Reject the Null
There is NOT enough evidence to conclude that the mean time teenagers spend on the phone per week is higher than 4.5 hours.
Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of teen girls smoke to stay thin? Use a 0.01 level of significance.
What is the p-value, decision, and conclusion?
p-value: 0.9937
Fail to Reject the Null
There is not enough evidence to conclude that more than thirty percent of teen girls smoke to stay thin.
We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the different for White females and Black females in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for White females is 4,930. Five hundred eighty were aged 15 to 24. The estimate for Black females is 330. Forty were aged 15 to 24. Perform a hypothesis test at the 0.01 significance level to determine if the the proportions of female suicide victims for ages 15 to 24 are the different for White females and Black females in the United States.
State the H0, H1, p-value, Decision, Conclusion
H0:P1=P2 (1 - White Female, 2- Black Female)
H1: P1/=P2
p-value: 0.8458
Fail to Reject the Null
There is not enough evidence to conclude the proportions of female suicide victims for ages 15 to 24 are the different for White females and Black females in the United States.
A recent debate about where in the United States skiers believe the skiing is best prompted a survey. The results of the survey are found in Rguroo (Skiing) Test to see if the best ski area is independent of the level of the skier at the 0.05 significance level.
State the p value.
p-value: 0.0324
Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a population standard deviation of 0.8 seconds. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims. For the 15 swims, Jeffrey's mean time was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preset α = 0.05. Assume that the swim times for the 25-yard freestyle are normal.
State the H0, H1, p-value, decision, and conclusion
H0: μ = 16.43 Ha: μ < 16.43
p-value = 0.0187
reject H0
There is enough evidence to conclude that Jeffrey's mean time to swim the 25-yard freestyle is less than 16.43 seconds.
From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is less than 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?
What is the Null and Alternate Hypothesis Statements? Also, what type of test will you run and why?
H0: M=19
H1: M<19
Z Test, because Population Standard Deviation is given.
A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 EVC students and finds that 11 attended the midnight showing. Test this claim at the 0.10 level.
What is the null and alternate hypothesis statements?
H0: P=0.20
H1: P<0.20
Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. The data are recorded in the Rguroo table (Cholesterol). Test to see if there is a change in cholesterol level after going on a low-fat diet at the 0.01 significance level?
State H0, H1, p-value, Decision, Conclusion
H0: Md=0
H1: Md/=0
p-value: 0.2706
Fail to reject the null
There is not enough evidence to conclude there is a change in cholesterol level after going on a low-fat diet.
A recent debate about where in the United States skiers believe the skiing is best prompted a survey. The results of the survey are found in Rguroo (Skiing) Test to see if the best ski area is independent of the level of the skier at the 0.05 significance level.
State the Decision and the Conclusion.
Reject the Null.
There is enough evidence to conclude that the best ski area and level of skier are associated.
Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65; 65; 70; 67; 66; 63; 63; 68; 72; 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution.
State H0, H1, p-value, decision, conclusion.
H0: μ = 65 Ha: μ > 65
p-value = 0.0396
reject H0
There is enough evidence to conclude that the mean test score is greater than 65, just as the math instructor thinks.
From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is less than 19. The sample mean was 18.1. Do the data support the claim at the 5% level?
What is the p-value, the decision, and the conclusion?
p-value: 0.0034
Reject the Null
There is enough evidence to conclude that the mean starting age for smoking is less than 19.
A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She randomly surveys 84 EVC students and finds that 11 attended the midnight showing. Test this claim at the 0.10 level. What is the p-value, decision, and conclusion?
p-value: 0.0568
Reject the null
There is enough evidence to conclude fewer than 20% of Evergreen Valley College students attend the opening night.
A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is different at the 0.05 significance level?
State H0, H1, p-value, decision, conclusion
H0: P1=P2 (1: Cabrillo, 2: Lake Tahoe)
H1: P1/=P2
p-value: 0.000018
Reject the null
There is enough evidence to conclude that the percent of Hispanic students at the two colleges is different.
Elizabeth is a financial adviser for a car dealership with locations throughout the country. She wondered if sales of convertibles are relatively higher in warm weather cities than in cold weather cities. To test her theory, she collected random samples of cars sold throughout a one-year period for locations in San Diego and Boston. Out of 400 cars sold in San Diego, 52 were convertibles, and 34 out of 400 cars sold in Boston were convertibles. Is there evidence at the 0.05 significance level that the proportion of convertibles sold in San Diego is greater than the proportion in Boston? Assume that the conditions for the hypothesis test are satisfied. Let San Diego cars correspond to population 1 and Boston cars correspond to population 2.
State the H0, H1, p-value, decision, conclusion
(1: warm weather cities, 2: cold weather cities)
H0: P1=P2
H1: P1>P2
p-value: 0.01996 or 0.02
Reject the Null
There is enough evidence to conclude the proportion of convertibles sold in San Diego is greater than the proportion in Boston.
A study is done by a community group in two neighboring colleges to determine which one graduates students with more math classes. College A samples 11 graduates. Their average is four math classes with a standard deviation of 1.5 math classes. College B samples nine graduates. Their average is 3.5 math classes with a standard deviation of one math class. The community group believes that a student who graduates from college A has taken more math classes, on the average. Both populations have a normal distribution. Test at a 1% significance level.
State H0, H1, p-value, decision, conclusion.
A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test your claim at the 5% level of significance.
State the following:
H0,H1,test type, pvalue,Decision,Conclusion.
H0:M=4
H1:M>4
T test
pvalue: 0.0380
Reject the null
There is enough evidence to conclude that the mean IQ of trout is greater than 4.
The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. Use a 0.05 level of significance.
State the null, alternate, p-value, decision, and conclusion.
H0: P=0.095
H1: P<0.095
p-value: 0.1969
Fail to reject the null
There is not enough evidence to conclude that the true of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.
A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test this claim at the 0.05 significance level.
State H0, H1, p-value, decision, conclusion
(1: 4 yr, 2: 2 yr)
H0: M1=M2
H1: M1>M2
p-value: 0.4024
Fail to Reject the Null
There is not enough evidence to conclude that the mean enrollment at four–year colleges is higher than at two–year colleges in the United States.
A marine biologist wanted to measure the masses of the males and females of a particular species of fish in different regions of a bay. She collected 10 samples of fish from different regions and measured their average masses. Assume that the populations are normally distributed.
The biologist tests the paired data, where α=0.05, in order to evaluate the claim that the true mean difference in masses between male and female fish are not equal to zero. Data can be found on Rguroo (male and female fish).
State the H0, H1, p-value, decision, conclusion
H0: Md=0
H1: Md/=0
pvalue = 0.0680
Fail to Reject the Null
There is not enough evidence to conclude that the true mean difference in masses between male and female fish are not equal to zero.
In a volunteer group, adults 21 and older volunteer from one to nine hours each week to spend time with a disabled senior citizen. The program recruits among community college students, four-year college students, and nonstudents. In Rguroo table (Volunteer Type and Hours) is a sample of the adult volunteers and the number of hours they volunteer per week.
Is the number of hours volunteered independent of the type of volunteer? Test at the 0.05 significance level.
State H0, H1, p-value, decision, conclusion.
H0: Volunteer type and volunteer hours are independent.
H1: Volunteer type and volunteer hours are not independent.
p-value: 0.0113
Reject the null
There is enough evidence to conclude volunteer type and volunteer hours are not independent.