Math 141 Terms
The correlation coefficient is always a number between _______.
-1 and 1
A significance level that is often used in hypothesis testing by researchers and statisticians is _____.
0.05.
If the conditions of a survey sample satisfy those required by the Central Limit Theorem, then there is a 95% probability that a sample proportion will fall within how many standard errors of the population proportion?
2 standard errors
The symbol in the null hypothesis is always _______.
=.
Which of the following is an appropriate interpretation of a confidence interval?
A range of plausible values for the population parameter.
Is it possible for a standard deviation to be equal to zero? Explain.
A standard deviation can be zero if all the values are the same.
According to the Empirical Rule, ________ will be within two standard deviations of the mean.
According to the Empirical Rule, approximately 95% of the observations will be within two standard deviations of the mean.
When computing the t-statistic, one divides by an estimate of the standard error. Why does one not divide by the true standard error?
Because in real life one almost never knows the value of the population standard deviation.
How are confidence intervals reported by professional statisticians and the press?
Both A and B
When writing a regression equation, which of the following is not a name for the x-variable?
Dependent variable
Explain the difference between sampling with replacement and sampling without replacement. Suppose you had the names of 10 students, each written on a 3 by 5 notecard, and want to select two names. Describe both procedures.
Describe sampling with replacement. Choose the correct answer below. Draw a notecard, note the name, replace the notecard and draw again. It is possible the same student could be picked twice. Describe sampling without replacement. Choose the correct answer below. Draw a notecard, note the name, do not replace the notecard and draw again. It is not possible the same student could be picked twice.
What are statistics sometimes called?
Estimates
Recently, a health organization estimated that the flu vaccine was 68% effective against the influenza B virus. An immunologist suspects that the current flu vaccine is less effective against this virus. Pick the correct pair of hypotheses the immunologist could use to test this claim.
H0: p=0.68 Ha: p<0.68
A law association estimated that 85.1% of law school graduates last year found employment. An economist thinks the current employment rate for law school graduates is different from the rate last year. Pick the correct pair of hypotheses the economist could use to test this claim.
H0: p=0.851 Ha: p≠0.851
A larger firm is considering acquiring a small bookstore. An analyst for the firm, noting that there is a strong, positive relationship between the number of sales people working and the amount of sales, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion justified? What alternative explanations can you offer? Use appropriate statistics terminology.
His conclusion is not justified. Correlation does not demonstrate causation. When there is a strong correlation, it is not justifiable to conclude that the predictor variable caused the change. The analyst's argument is that sales staff causes sales. However, it may be the reverse, that more people were hired as sales increased.
Which of the following is measured by the test statistic?
How far away the observed mean lies from the hypothesized value of the population mean.
A standard unit measures which of the following?
How many standard deviations away an observation is from the mean
Chapman University conducts an annual Survey of American Fears. In 2017 the survey used a sample size of 1207 people, who were selected at random from Americans of all ages. One of the survey findings was that 16% believe that Bigfoot is a real creature.
Identify the sample. Choose the correct answer below. The sample is the 1207 participants. Identify the population. Choose the correct answer below. The population is people in the United States. Is the value 16% a parameter or a statistic? What symbol would be used for this value? The value 16% is a statistic. 16%=p̂
The Centers for Disease Control and Prevention (CDC) conducts an annual Youth Risk Behavior Survey, surveying over 15,000 high school students. The 2015 survey reported that, while cigarette use among high school youth had declined to its lowest levels, 24% of those surveyed reported using e-cigarettes. Identify the sample and population. Is the value 24% a parameter or a statistic? What symbol would we use for this value?
Identify the sample. Choose the correct answer below. The sample is the over 15,000 high school students. Identify the population. Choose the correct answer below. The population is high school students. Is the value 24% a parameter or a statistic? What symbol would be used for this value? The value 24% is a statistic 24%=p̂
In 1994, major league baseball players went on strike. At the time, the average salary was $1,049,589, and the median salary was $337,500. If you were representing the owners, which summary would you use to convince the public that a strike was not needed? If you were a player, which would you use? Why was there such a large discrepancy between the mean and median salaries? Explain.
If you were representing the owners, you would use the average salary to convince the public that a strike was not needed. If you were a player, you would use the median salary to convince the public that a strike was needed. The average and median salaries differ so greatly because the distribution of salaries is skewed right.
A small p-value does what?
It discredits the null hypothesis.
If there is a positive association between number of years studying spelling and ear size (for children), does that prove that larger ears cause more studying of spelling, or vice versa? Can you think of a hidden variable that might be influencing both of the other variables?
It does not prove causation, because older children have larger ears and have studied spelling longer. Larger ears do not cause an increase in years of studying. The hidden variable is age.
When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?
It is a null hypothesis, since it is assumed to be true until evidence can prove otherwise.
A practically significant result has which of the following pairs of attributes?
It is both statistically significant and meaningful.
In 2008, a highway safety administration reported that the number of pedestrian fatalities in City A was 65 and that the number in City B was 45. Can we conclude that pedestrians are safer in City B? Why or why not?
No, in order to compare the fatalities the statistics must include the number of fatalities per pedestrian. There may be fewer pedestrians in City B causing the difference.
If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature?
No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.
Name two measures of the center of a distribution, and state the conditions under which each is preferred for describing the typical value of a single data set.
One measure of the center of a distribution is the mean. This measure is preferred when the distribution is relatively symmetric. One measure of the center of a distribution is the median. This measure is preferred when the distribution is strongly skewed.
Values so large or so small that they do not fit into the pattern of the distribution are called what?
Outliers
What is a numerical value that characterizes some aspect of a population?
Parameter
What is the term for a group of objects or people to be studied?
Population
Hypotheses are always statements about which of the following?
Population parameters
"Relative frequency" is the same as which of the following?
Proportion
When a national sample of heights of kindergarten children was taken, a student was told that she was in the 25th percentile. Explain what that means.
She is taller than 25 percent of all kindergarten children.
Is simple random sampling usually done with or without replacement?
Simple random sampling is usually done withoutreplacement, which means that a subject cannot be selected for a sample more than once.
What is the standard deviation of the sampling distribution called?
Standard error
Which of the following best describes hypotheses?
Statements about population parameters
A random sample of 25 private universities was selected. A 95% confidence interval for the mean in-state tuition costs at private universities was (22,501, 32,664).Which of the following is a correct interpretation of the confidence level? a. There is a 95% probability that the mean in-state tuition costs at a private university is between $22,501 and $32,664. b. In about 95% of the samples of 25 private universities, the confidence interval will contain the population mean in-state tuition.
Statement (b) correctly interprets the confidence level.
The average birth weight of elephants is 230 pounds. Assume that the distribution of birth weights is Normal with a standard deviation of 60 pounds. Find the birth weight of elephants at the 85th percentile.
The birth weight of elephants at the 85th percentile is 292 pounds. (Round to the nearest integer as needed.)
A city provides an open data set of the number of WiFi sessions at all of its public libraries. For 2014, there were an average of 480,164.8 WiFi sessions per month at all the public libraries in this city. What is the correct notation for the value 480,164.8?
The correct notation for the value 480,164.8 is μ
A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more plows whenever it snows because, he says, that will increase business. Comment on the director's conclusion.
The director is wrong. The lurking variable here is the severity of the blizzard. A more severe blizzard calls for more plows and keeps people at home, where they are more likely to make online purchases.
The distribution of in-state annual tuition for all colleges and universities in the United States is bimodal. What is one possible reason for this bimodality?
The distribution might be bimodal because private colleges and public colleges tend to differ in amount of tuition.
Predict the shape of the distribution of the numbers of times a group of 500 people eat dinner in one week.
The distribution will be left-skewed. Most people will report eating dinner every day, with a few reporting various values less than 7.
A group of 80 drivers in a large city is asked for the number of parking tickets they received in the previous month. What shape do you think this distribution will have? Explain.
The distribution will be right-skewed. Most people will have no tickets, but there will be a few people with 1, 2, 3, or more tickets.
A human resources manager for a large company takes a random sample of 50 employees from the company database. She calculates the mean time that they have been employed. She records this value and then repeats the process: She takes another random sample of 50 names and calculates the mean employment time. After she has done this 1000 times, she makes a histogram of the mean employment times. Is this histogram a display of the population distribution, the distribution of a sample, or the sampling distribution of means?
The histogram is a display of the sampling distribution of means.
Several times during the year, the U.S. Census Bureau takes random samples from the population. One such survey is the American Community Survey. The most recent such survey, based on a large (several thousand) sample of randomly selected households, estimates the mean retirement income in the United States to be $21,201 per year. Suppose we were to make a histogram of all of the retirement incomes from this sample. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?
The histogram would be a display of the distribution of a sample.
The label on a can of mixed nuts says that the mixture contains 60% peanuts. After opening a can of nuts and finding 32 peanuts in a can of 50 nuts, a consumer thinks the proportion of peanuts in the mixture differs from 60%. The consumer writes these hypotheses: H0: p=0.60 and Ha: p=0.64, where p represents the proportion of peanuts in all cans of mixed nuts from this company. Are these hypotheses written correctly? Correct any mistakes as needed.
The hypotheses are not correct. They should be H0: p=0.60 and Ha:p≠0.60.
To form a confidence interval, what value is added to and subtracted from the estimator?
The margin of error
In a right-skewed distribution, which of the following is true?
The mean tends to be greater than the median.
What is true in a hypothesis test, the farther the test statistic is from 0?
The more the null hypothesis is discredited
In hypothesis testing, the null hypothesis is best described by which of the following statements?
The null hypothesis always gets the benefit of the doubt and is assumed to be true throughout the hypothesis testing procedure.
Which of the following phrases should not be used when writing a conclusion to a hypothesis test?
The null hypothesis is accepted as true.
The null hypothesis is always a statement about what?
The null hypothesis is always a statement about a population parameter.
In hypothesis testing, what does an extreme value for the test statistic indicate?
The null hypothesis is not true
If an observation has a z-score of 0, this means which of the following?
The observation is equal to the mean.
Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m. The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do. What information is missing that might contradict this claim?
The percentage of female students in the two classes is unknown. There may be more females in the 8 a.m. because there are more students in the 8 a.m. class than the 10 a.m. class. This claim could be true only if the classes were the same size.
What is the mean of the sampling distribution of the sample mean?
The population mean
When taking samples from a population and computing the proportion of each sample, which of the following values is always the same?
The population proportion
A weight-loss diet claims that it causes weight loss by eliminating carbohydrates (breads and starches) from the diet. To test this claim, researchers randomly assign overweight subjects to two groups. Both groups eat the same amount of calories, but one group eats almost no carbs, and the other group includes carbs in their meals. After 2 months, the researchers test the claim that the no-carb diet is better than the usual diet. They record the proportion of each group that lost more than 5% of their initial weight. They then announce that they failed to reject the null hypothesis. Which of the following are valid interpretations of the researchers' findings?
The researchers did not see enough evidence to conclude that the no-carb diet was more effective. There were no significant differences in effectiveness between the no-carb diet and the carb diet.
In hypothesis testing, what does a negative test statistic mean?
The sample proportion was less than the assumed population proportion in the null hypothesis
Is it possible for a standard deviation to be negative? Explain.
The standard deviation cannot be negative because in the calculation all differences from the mean are squared, making all distances positive values.
In the most recent summer Olympics, do you think the standard deviation of the running times for all men who ran the 100-meter race would be larger or smaller than the standard deviation of the running times for the men's marathon? Explain.
The standard deviation for the 100-meter event would be less. All the runners come to the finish line within a few seconds of each other. In the marathon, the runners can be quite widely spread after running that long distance.
Which of the following does the confidence level measure?
The success rate of the method of finding confidence intervals
Select the correct choice that completes the sentence below.
The sum of the deviations about the mean always equals zero.
Software packages often give the choice to run a two-sample t-test by "pooling" the standard deviations. Which of the following statements is correct?
The unpooled version is preferred over the other version because the pooled version works well only in special circumstances
The value that would be right in the middle if you were to sort the data from smallest to largest is called the ______.
The value that would be right in the middle if you were to sort the data from smallest to largest is called the median.
A psychologist is interested in testing whether offering students a financial incentive improves their video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video game is greater with a financial incentive than without. Her null hypothesis is that the probability of getting to this level is the same with or without a financial incentive. The alternative is that this probability is greater. She gets a p-value from her hypothesis test of 0.003. What is the best interpretation of the p-value?
The p-value is the probability of getting a result as extreme as or more extreme than the one obtained, assuming that financial incentives are not effective in this context.
When comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, will you get a smaller p-value if the sample proportions are close together or if they are far apart? Explain.
The p-value will be smaller if the sample proportions are far apart because a larger difference results in a larger absolute value of the numerator of the test statistic.
When comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, will you get a smaller p-value with a larger sample size or a smaller sample size? Explain.
The p-value will be smaller with a larger sample size because a larger sample results in a smaller standard error, which is the denominator of the test statistic.
The multiplier used to compute the margin of error for a confidence interval for a population mean is based on which of the following?
The t-distribution
In hypothesis testing, when should the null hypothesis be rejected?
When the p-value is less than the significance level
When should a confidence interval approach be used?
Whenever one is estimating the value of a population parameter on the basis of a random sample from that population.
A magazine advertisement claims that wearing a magnetized bracelet will reduce arthritis pain in those who suffer from arthritis. A medical researcher tests this claim with 233 arthritis sufferers randomly assigned to wear either a magnetized bracelet or a placebo bracelet. The researcher records the proportion of each group who report relief from arthritis pain after 6 weeks. After analyzing the data, he fails to reject the null hypothesis. What are valid interpretations of his findings?
Which of the following are valid interpretations of his findings? There may be more than one correct answer. Select all answers that apply. There's insufficient evidence that the magnetized bracelets are effective at reducing arthritis pain. There were no statistically significant differences between the magnetized bracelets and the placebos in reducing arthritis pain.
A psychologist is interested in testing whether offering students a financial incentive improves their video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video game is greater with a financial incentive than without. Her null hypothesis is that the probability of getting to this level is the same with or without a financial incentive. The alternative is that this probability is greater. She gets a p-value from her hypothesis test of 0.003. What is the best interpretation of the p-value?
Which of the following is the best interpretation of the p-value? Choose the correct answer below. The p-value is the probability of getting a result as extreme as or more extreme than the one obtained, assuming that financial incentives are not effective in this context.
A researcher carried out a hypothesis test using a two-tailed alternative hypothesis. Which of the following z-scores is associated with the smallest p-value? Explain. i. z=0.43 ii. z=−0.98 iii. z=−2.31 iv. z=3.22
Which z-score has the smallest p-value? z=3.22 Explain. The z-score farthest from 0 has the smallest tail area and thus has the smallest p-value.
Since, in general, the longer a car is owned the more miles it travels one can say there is a _______ between age of a car and mileage.
a positive association
A random sample of 35 baseball players from the a baseball league's season was taken and the sample data were used to construct 90% and 95% confidence intervals for the population mean. One interval was (25.2, 42.2). The other interval was (24.0, 43.4). a. How would a 99% interval compare? Would it be narrower than both, wider than both, or between the two in width? Explain. b. If we wanted to use a 99% confidence level and get a narrower width, how could we change our data collection?
a. A 99% interval would be wider than both—the value of t* for a 99% interval is greater than both that for a 90% interval and that for a 95% interval. b. Increase the number of observations by an appropriate amount.
According to an online source, the average shower in a country lasts 9.2 minutes. Assume that this is correct and assume the standard deviation of 3 minutes. Complete parts (a) through (c) below.
a. Do you expect the shape of the distribution of shower lengths to be Normal, right-skewed, or left-skewed? Explain your reasoning. The distribution will be right-skewed because the values will be mostly small but there will be a few very large values. b. Suppose we survey a random sample of 100 people to find the length of their last shower. We calculate the mean length from this sample and record the value. We repeat this 500 times. What will be the shape of the distribution of these sample means? The distribution will be approximately Normal because the values will be distributed symmetrically. c. Refer to part (b). What will be the mean and standard deviation of the distribution of these sample means? The mean will be 9.2 minutes and the standard deviation will be 0.3 minutes. (Type integers or decimals rounded to one decimal place as needed.)
The mean age of all 2527 students at a small college is 22.4 years with a standard deviation of 3.3 years, and the distribution is right-skewed. A random sample of 4 students' ages is obtained, and the mean is 22.8 with a standard deviation of 2.8 years.
a. Find μ, σ, s, and x̄. μ=22.422.4 σ=3.33.3 x=22.822.8 s=2.82.8 b. Is μ a parameter or a statistic? The value of μ is a parameter because it is found from the population. c. What would be the shape of the approximate sampling distribution of many means, each from a sample of 4 students? Right-skewed
The mean age of all 667 used cars for sale in a newspaper one Saturday last month was 7.4 years, with a standard deviation of 7.2 years. The distribution of ages is right-skewed. For a study to determine the reliability of classified ads, a reporter randomly selects 50 of these used cars and plans to visit each owner to inspect the cars. He finds that the mean age of the 50 cars he samples is 8.0 years and the standard deviation of those 50 cars is 5.6 years.
a. From the problem statement, which of the values 7.4, 7.2, 8.0, and 5.6 are parameters and which are statistics? The value 7.4 is a parameter. The value 7.2 is a parameter. The value 8.0 is a statistic. The value 5.6 is a statistic. b. Find μ, σ, s, and x̄. μ=7.47.4 σ=7.27.2 s=5.65.6 x̄=8.08.0 c. What would be the shape of the approximate sampling distribution of a large number of means, each from a sample of 50 cars? Normal
Suppose it is known that 20% of students at a certain college participate in a textbook recycling program each semester. Complete parts (a) and (b) below.
a. If a random sample of 40 students is selected, do we expect that exactly 20% of the sample participates in the textbook recycling program? Why or why not? Choose the correct answer below. We do not expect that exactly 20% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population proportion, but it will vary by the sample error from sample to sample. b. Suppose we take a sample of 400 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20%: the proportion from a sample size of 40or the proportion from a sample size of 400? Explain your reasoning. Choose the correct answer below. The sample with size 400 will be closer to 20% because a larger sample size has a smaller standard error.
a. In your own words, describe to someone who knows only a little statistics how to recognize when an observation is an outlier. What action(s) should be taken with an outlier? b. Which measure of the center (mean or median) is more resistant to outliers, and what does "resistant to outliers" mean?
a. Outliers are observed values far from the main group of data. In a histogram they are separated from the others by space. Outliers must be looked at in closer context to know how to treat them. If they are mistakes, they might be removed or corrected. If they are not mistakes, you might do the analysis twice, once with and once without the outliers. b. The median is more resistant, which indicates that it usually changes less than the mean when comparing data with and without outliers.
A city provides an open data set of commercial building energy use. Each row of the data set represents a commercial building. A sample of 250 buildings from the data set has a mean floor area of 36,291 square feet. Of the sample, 26% were office buildings. a. What is the correct notation for the value 36,291? b. What is the correct notation for the value 26%?
a. The correct notation for the value 36,291 is x̄ b. The correct notation for the value 26% is p̂
Drivers in Alaska drive fewer miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Alaska is 9109 miles. Assume the standard deviation is 3900 miles. A random sample of 100 licensed drivers in Alaska is selected and the mean number of miles driven yearly for the sample is calculated. a. What value would we expect for the sample mean? b. What is the standard error for the sample mean?
a. The expected sample mean is 91099109 miles, because the sample mean is an unbiased estimator of the population mean. (Round to the nearest integer as needed.) b. What is the standard error for the sample mean? The standard error for the sample mean is 390.0 miles. (Type an integer or decimal rounded to the nearest tenth as needed.)
A study of all the students at a small college showed a mean age of 20.9 and a standard deviation of 1.5 years. a. Are these numbers statistics or parameters? Explain. b. Label both numbers with their appropriate symbol (such as x̄, μ, s, or σ).
a. The numbers are parameters because they are for all the students, not a sample. b. Choose the correct labels below. μ=20.9 σ=1.5
A survey of 100 random full-time students at a large university showed the mean number of semester units that students were enrolled in was 17.3 with a standard deviation of 2.1 units. a. Are these numbers statistics or parameters? Explain. b. Label both numbers with their appropriate symbol (such as x̄, μ, s, or σ).
a. The numbers are statistics because they are for a sample of students, not all students. b. Choose the correct labels below. x̄=17.3 s=2.1
Indicate which variable you think should be the predictor (x) and which variable should be the response (y). Explain your choices. a. A researcher measures subjects' stress levels and blood pressures. b. Workers who commute by car record the length of their commutes (in miles) and the amount spent monthly on gasoline purchases. c. Amusement parks record the heights and maximum speeds of roller coasters.
a. The predictor is stress level. The response is blood pressure. The subjects' blood pressures are likely to be explained by their stress levels; higher stress is associated with higher blood pressure. b. The predictor is commute length. The response is monthly gasoline purchases. Workers with longer commutes will need more gas to get to and from work; longer commute length is associated with higher gas purchases. c. The predictor is height. The response is maximum speed. A roller coaster has a higher speed if it starts from a greater height; taller height is associated with greater maximum speed.
Two symbols are used for the mean: μ and x̄. a. Which represents a parameter and which a statistic? b. In determining the mean age of all students at your school, you survey 30 students and find the mean of their ages. Is this mean x̄ or μ?
a. The symbol μ represents a parameter and x̄ represents a statistic. b. The mean is x̄.
A random sample of likely voters showed that 62% planned to vote for Candidate X, with a margin of error of 1 percentage points and with95% confidence. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage of voters who plan to vote for Candidate X. b. Is there evidence that Candidate X could lose? c. Suppose the survey was taken on the streets of a particular city and the candidate was running for president of the country that city is in. Explain how that would affect your conclusion.
a. Which of the following statements best describes the confidence interval for the percentage of voters who plan to vote for Candidate X? I am 95% confident that the population percentage of voters supporting Candidate X is between 61% and 63%. b. Is there evidence that Candidate X could lose? There is no evidence that the candidate could lose. The reason there is no evidence is because the interval is entirely above 50%. c. Which of the following is the best explanation on how the survey would affect your conclusion? A sample from this particular city would not be representative of the entire country and would be worthless in this context.
A friend is tested to see whether he can tell bottled water from tap water. There are 60 trials (half with bottled water and half with tap water), and he gets 33 right. a. Determine the null hypothesis. b. Determine the alternative hypothesis.
a. p=0.50 b. p>0.50
The process of representing categorical variables with numbers (such as letting a 1 represent "smoker" and a 0 represent "non-smoker") is called _______.
coding.
The _______ is a number that measures the strength of the linear association between two numerical variables.
correlation coefficient
As the sample size is increased, the spread of the sample means _______.
decreases.
The spread of the distribution of the sample mean is _______ the spread of the population.
much smaller than
In statistical inference, measurements are made on a ______ and generalizations are made to a ________.
sample population.
If the mean and the median of a distribution are approximately the same, then the shape of the distribution is likely to be _______.
symmetric.
The standard deviation of all professional NBA basketball players is 29.9 pounds. A sample of 70 professional basketball players has a standard deviation of 29.8 pounds. Which number is σ and which number is s?
σ is 29.9 pounds and s is 29.8 pounds.
If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? Why or why not?
No, if the p-value is sufficiently small, the null hypothesis is unlikely to be true, but unlikely is not the same as impossible.
When, in a criminal court, a defendant is found "not guilty," is the court saying with certainty that he or she is innocent? Explain.
No, the court is only saying that there is not enough evidence to show guilt.
If we do not reject the null hypothesis, is it valid to say that we accept the null hypothesis? Why or why not?
No, we have only shown that we do not have enough evidence to reject it.
