Exam 4 (Chapters 8, 9 and 12.2)
Which of the following is NOT a criterion for making a decision in a hypothesis test?
If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
The ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.
Test statistic
Which of the following is NOT true about P-values in hypothesis testing?
The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.
Assume that the significance level is α=0.05. Use the given information to find the P-value and the critical value(s). The test statistic of z=2.11 is obtained when testing the claim that p>0.4.
1) Find 2.11 on page 1 of the table 2) Find 0.05 on table numbers *If p > number, it will be positive. If p < number, it will be negative. If p=number, it will be two values *If p= or not equals a number, multiply P-value by 2
Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d=x−y, find d over bar, sd, the t test statistic, and the critical values to test the claim that μd=0. x y 5 6 4 5 8 6 7 10 10 6 6 11 6 5 12 8
1) Find d over bar a. Subtract the x values from the y values. SUMd=1 b. How many observations were made? (n) n=8 c. Solve for d over bar =SUMd/n=.125 2) Find the variance a. Find SUM(d-d over bar)^2 =72.875 b. Solve for variance Use formula: s^2d=(SUM(d-d over bar)^2)/(n-1) c. s^2d=72.875/(8-1)=10.410714 d. Sqrt(10.410714) =3.227 3) find the t statistic a. use formula: t=(d over bar-μd)/(sd)/(sqrt(n)) b. solve 0.125-0/s.227/sqrt(8) =.110 3) Find critical value look up on chart +-2.365
In 1997, a survey of 820 households showed that 154 of them use e-mail. Use those sample results to test the claim that more than 15% of households use e-mail. Use a 0.05 significance level. Use this information to answer the following questions.
H0: p=0.15 H1: p>0.15 What is the conclusion? There is sufficient evidence to support the claim that more than 15% of households use e-mail. Is the conclusion valid today?Why or why not? No, the conclusion is not valid today because the population characteristics of the use of e-mail are changing rapidly.
Listed below are the heights of candidates who won elections and the heights of the candidates with the next highest number of votes. The data are in chronological order, so the corresponding heights from the two lists are matched. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of all "winner/runner-up" differences. Does height appear to be an important factor in winning an election? -1.10<μ<2.85 Based on the confidence interval, does height appear to be an important factor in winning an election?
NO, because the confidence interval INCLUDES 0
The _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.
Null
Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. Friday the 6th: Friday the 13th: 10 14 7 13 12 14 12 11 3 5 4 11
A) What are the hypotheses for this test? Let μd be the *mean of the differences* in the numbers of hospital admissions resulting from motor vehicle crashes for the population of all pairs of data. H0: μd=0 H1: μd≠0 B) State the result of the test. Choose the correct answer below. There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.
The claim is that the white blood cell counts of adult females are normally distributed, with a standard deviation equal to 2.97. A random sample of 17 adult females has white blood cell counts with a mean of 6.78 and a standard deviation of 2.73. Find the value of the test statistic.
x^2=(n-1)s^2/σ^2 s^2=2.73 σ=2.97 n=17
The claim is that the IQ scores of statistics professors are normally distributed, with a mean greater than 127. A sample of 10 professors had a mean IQ score of 131 with a standard deviation of 12. Find the value of the test statistic.
Wants to find a mean, so use t formula t=x with bar-μ/s/sqrt(n) x with bar=131 μ=127 s=12 n=10
A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "before−after" differences. Does hypnotism appear to be effective in reducing pain? Before After 7.9 6.5 5.0 2.7 6.9 7.7 12.6 8.5 9.5 8.9 5.7 6.6 8.5 3.6 5.5 2.4 Construct a 95% confidence interval for the mean of the "before−after" differences. .04l<μ<3.64 Does hypnotism appear to be effective in reducing pain?
Yes, because the confidence interval DOES NOT include zero and is ENTIRELY GREATER than zero.
The accompanying data table contains chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. Shown are the technology results for analysis of variance of this data table. Assume that a researcher plans to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Complete parts (a) and (b) below. a. What characteristic of the data specifically indicates that one-way analysis of variance should be used? b. If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?
A. The measurements are categorized according to the one characteristic of size. B. The method is based on estimates of a common population variance.
Claim: The mean weight of beauty pageant winners is 114 pounds. A study of 15 randomly selected beauty pageants resulted in a mean winner weight of 113 pounds. a. Express the original claim in symbolic form. b. Identify the null and the alternative hypotheses.
A. μ=114 B. H0: μ=114 H1= μ≠114
Claim: High school teachers have incomes with a standard deviation that is more than $22,250. A recent study of 138 high school teacher incomes showed a standard deviation of $23,250. a. Express the original claim in symbolic form. b. Identify the null and the alternative hypotheses that should be used to arrive at a conclusion that supports the claim.
A. σ > $22,250 B. H0: σ = $22,250 H1= σ > $22,250
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2786 occupants not wearing seat belts, 34 were killed. Among 7715 occupants wearing seat belts, 18 were killed. Use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.
Because the confidence interval limits *do not include* 0, it appears that the two fatality rates are *not equal.* Because the confidence interval limits include *only positive values,* it appears that the fatality rate is *higher* for those not wearing seat belts. The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts.
When games were sampled throughout a season, it was found that the home team won 126 of 199 soccersoccer games, and the home team won 62 of 88 lacrosselacrosse games. The result from testing the claim of equal proportions are shown on the right. Does there appear to be a significant difference between the proportions of home wins? What do you conclude about the home field advantage?
Does there appear to be a significant difference between the proportions of home wins? (Use the level of α=0.05.) Since the p-value is large, there is not a significant difference. B. What do you conclude about the home field advantage? (Use the level of significance α=0.05.) The advantage appears to be about the sameabout the same for soccer and lacrosse.
A coin mint has a specification that a particular coin has a mean weight of 2.5 g. A sample of 34 coins was collected. Those coins have a mean weight of 2.49396 g and a standard deviation of 0.01318 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the coins appear to conform to the specifications of the coin mint?
H0: μ=2.52.5 g H1: μ≠2.52.5 g Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g. Do the coins appear to conform to the specifications of the coin mint? No, since the coins seem to come from a population with a mean weight different from 2.5 g.
Which of the following statements are true concerning the mean of the differences between two dependent samples (matched pairs)?
If one wants to use a confidence interval to test the claim that μd>0 with a 0.01 significance level, the confidence interval should have a confidence level of 98%. If one has fifteen matched pairs of sample data, there is a loose requirement that the fifteen differences appear to be from a normally distributed population.
The _____________ states that if, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
Rare Event Rule
A sample of colored candies was obtained to determine the weights of different colors. The ANOVA table is shown below. It is known that the population distributions are approximately normal and the variances do not differ greatly. Use a 0.05 significance level to test the claim that the mean weight of different colored candies is the same. If the candy maker wants the different color populations to have the same mean weight, do these results suggest that the company has a problem requiring corrective action?
Should the null hypothesis that all the colors have the same mean weight be rejected? Yes, because the P-value is less than the significance level Does the company have a problem requiring corrective action? Yes, because it is likely that the candies do not have equal mean weights.
Which of the following is NOT a true statement about error in hypothesis testing?
A type I error is making the mistake of rejecting the null hypothesis when it is actually false.
A _____________ is a procedure for testing a claim about a property of a population.
Hypothesis test
Which of the following is NOT a principle of making inferences from dependent samples?
Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0.
Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis testing?
The lowercase symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.
When does a confidence interval support the conclusion of the test?
When it includes 0
The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 650 peas with 176 of them having yellow pods. Find the value of the test statistic.
z=^p−p/sprt((pq)/n) ^p=176/650 p=.25 n=650 q=.75 Proportions use z formula
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain.
The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the number of successes is at least 5 and the number of failures is at least 5.
Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population portions?
The sample is at least 5% of the population.
Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Actress age Actor age 19 50 30 45 24 60 50 53 29 39
1) Hypothesis? H0: μd=0 H1: μd≠0 2) Test statistic (t-value) and P-value a. Find d b. Use 1 var stats for differences c. T-test for difference 1 var stats data 3) What is the conclusion based on the hypothesis test? Since the P-value is *less* than the significance level, *reject* the null hypothesis. There *is* sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.
When subjects were treated with a drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Using a 0.05 significance level, is there sufficient evidence to support the claim that the drug is effective in lowering systolic blood pressure? Before After 210 179 195 176 190 156 189 155 202 190 155 156 205 143 157 152 183 144 169 186 175 162 194 162
A) Hypothesis? H0: μd=0 H1: μd>0 B) Since the P-value is *less* than the significance level, *reject* Upper H0. There is *sufficient* evidence to support the claim that the drug is effective in lowering systolic blood pressure.
Several students were tested for reaction times (in thousandths of a second) using their right and left hands. (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the subject.) Results from five of the students are included in the graph to the right. Use a 0.05 significance level to test the claim that there is no difference between the reaction times of the right and left hands Right hand Left hand 101 109 101 126 156 176 187 199 195 210
A) What are the hypotheses for this test? Let μd be the *mean of the differences* of the right and left hand reaction times. H0: μd=0 H1: μd≠0 B) What is the test statistic? a. Find d b. Use 1 var stats for differences c. T-test for difference 1 var stats data C) Identify the critical value(s). Select the correct choice below and fill the answer box within your choice. t=±2.776. D) What is the conclusion? There *is* enough evidence to warrant rejection of the claim that there is *no difference* between the reaction times of the right and left hands.
Assume a significance level of α=0.05 and use the given information to complete parts (a) and (b) below. The proportion of male golfers is more than 0.8. The hypothesis test results in a P-value of 0.185. a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?
A. Fail to reject H0 because the P-value is greater than α. B. There is not sufficient evidence to support the claim that the proportion of male golfers is more than 0.8.
Assume a significance level of α=0.05 and use the given information to complete parts (a) and (b) below. Original claim: Women have heights with a mean equal to 160.6 cm. The hypothesis test results in a P-value of 0.1665. a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?
A. Fail to reject H0 because the P-valueis greater than α. B. There is not sufficient evidence to warrant rejection of the claim that the mean height of women is equal to 160.6 cm.
In a random sample of males, it was found that 23 write with their left hands and 224 do not. In a random sample of females, it was found that 65 write with their left hands and 432 do not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below.
A. Hypothesis? H0: p1=p2 H1: p1<p2 B.Test statistic? Use Z2prop BUT make sure to add both numbers together to get n. C. What is the conclusion based on the confidence interval? Because the confidence interval limits *include* 0, it appears that the two rates of left-handedness are *equal.* There *is not* sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females. D. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females? The rate of left-handedness among males does not appear to be less than the rate of left-handedness among females.
A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. SEE iPAD FOR PICTURE
A. Hypothesis? H0: μ1=μ2 H1: μ≠μ2
A certain drug is used to treat asthma. In a clinical trial of the drug, 25 of 297 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 10% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below. 1-PropZTest p<0.1 z=−0.909072203 p=0.1816560071 p^=0.0841750842 n=297297
A. LEFT tailed test B. Test statistic z=-0.91 C. P-value? .1817 D. Null hypothesis? H0: p=0.1 E. Decide whether to reject the null hypothesis. Choose the correct answer below. *Fail to reject* the null hypothesis because the P-value is greater than the significance level, α. F. What is the final conclusion? There is not sufficient evidence to support the claim that less than 10% of treated subjects experienced headaches.
Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of settled medical malpractice suits is 0.23. a. Which of the following is a type I error? b. Which of the following is a type II error?
A. Reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23. B. Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.
In a recent poll, 805 adults were asked to identify their favorite seat when they fly, and 501 of them chose a window seat. Use a 0.05 significance level to test the claim that the majority of adults prefer window seats when they fly. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
H0: p=0.5 H1: p>0.5 What is the conclusion about the null hypothesis? Reject the null hypothesis because the P-value is less than or equal to the significance level, α. What is the final conclusion? There is sufficient evidence to support the claim that the majority of adults prefer window seats when they fly.
A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this writing, 969 babies were born to parents using the new method, and 890 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
H0: p=0.5 H1: p>0.5 What is the conclusion about the null hypothesis? Reject the null hypothesis because the P-value is less than or equal to the significance level, α. What is the final conclusion? There is sufficient evidence to support the claim that the new method is effective in increasing the likelihood that a baby will be a girl.
A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?
H0: μ1=μ2=μ3 H1: At least one of the three population means is different from the others. Yes, these data suggest that the third mile appears to take longer, and a reasonable explanation is that it has a hill
In a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 243.6 sec and a standard deviation of 55.07 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the manual?
H0: μ=210 sec H1: μ >210 sec State the final conclusion that addresses the original claim. Choose the correct answer below. Reject H0. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec. What do the results suggest about the advice given in the manual? The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.
Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test for a difference between the measurements from the two arms. What can be concluded? Right arm(mmHg) Left arm(mmHg) 144 173 151 164 135 178 135 152 139 134
Hypothesis H0: μd=0 H1: μd≠0 What is the conclusion based on the hypothesis test? Since the P-value is *greater* than the significance level, *fail to reject* the null hypothesis. There *is not* sufficient evidence to support the claim of a difference in measurements between the two arms.
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 304 people over the age of 55, 60 dream in black and white, and among 282 people under the age of 25, 16 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.
Hypothesis? H0: p1=p2 H1: p1>p2 Test statistic and P-value? (z) 2propZTest What is the conclusion based on the hypothesis test? The P-value is *less than* the significance level of α=0.05, so *reject* the null hypothesis. There is *sufficient* evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Confidence Interval? Enter data into Z2propconfidence What is the conclusion based on the confidence interval? Because the confidence interval limits *do not include* 0, it appears that the two proportions are *not equal.* Because the confidence interval limits include *only positive values*, it appears that the proportion of people over 55 who dream in black and white is *greater than* the proportion for those under 25. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation? No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.
-11.26 < μd < .46 (Round to two decimal places as needed.) Based on the confidence interval, can one reject the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected?
No, because the confidence interval includes zero.
Which of the following is NOT true about the tails in a distribution?
The inequality symbol in the alternative hypothesis points away from the critical region.
The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed? Type 1 Type 2 2026 2059 1948 1925 2132 2092 2517 2493 2178 2123 1906 1922 2215 2125 1545 1494
What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed? Because the confidence interval includes zero, there is not sufficient evidence to support farmer Joe's claim.
A genetic experiment involving peas yielded one sample of offspring consisting of 407 green peas and 125 yellow peas. Use a 0.01 significance level to test the claim that under the same circumstances, 26% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
What is the conclusion about the null hypothesis? Fail to reject the null hypothesis because the P-value is greater than the significance level, α. What is the final conclusion? There is not sufficient evidence to warrant rejection of the claim that 26% of offspring peas will be yellow.
In a study of treatments for very painful "cluster" headaches, 145 patients were treated with oxygen and 156 other patients were given a placebo consisting of ordinary air. Among the 145 patients in the oxygen treatment group, 120 were free from headaches 15 minutes after treatment. Among the 156 patients given the placebo, 25 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the claim that the oxygen treatment is effective.
What is the conclusion based on the confidence interval? Because the confidence interval limits *do not include* 0, it appears that the two cure rates are *not equal.* Because the confidence interval limits include *only positive* values, it appears that the cure rate is *higher* for the oxygen treatment than for the placebo. Based on the results, is the oxygen treatment effective? The results suggest that the oxygen treatment is effective in curing "cluster" headaches.
Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 47 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 92 of the 109 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.
What is the conclusion based on the confidence interval? Because the confidence interval limits *include 0*, there *does not* appear to be a significant difference between the two proportions. There *is not* evidence to support the claim that echinacea treatment has an effect. Based on the results, does echinacea appear to have any effect on the infection rate? Echinacea does not appear to have a significant effect on the infection rate.
A 0.05 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selection, the proportion of baby girls is greatergreater than 0.5. Assume that sample data consists of 120 girls in 225 births, so the sample statistic of 8/15 results in a z score that is 1 standard deviation aboveabove 0. Complete parts (a) through (h) below.
a. Identify the null hypothesis and the alternative hypothesis. H0: p=0.5 H1: p > 0.5 b. Is the test two-tailed, left-tailed, or right-tailed? To determine whether a test is two-tailed, left-tailed, or right-tailed, look at the alternative hypothesis and identify the region that supports that alternative hypothesis. Because the alternative hypothesis is H1: p > 0.5, the critical region lies in the extreme right region under the curve. Therefore, the test is right-tailed. c. What is the value of the test statistic? The problem statement gives that ^p=8/15 and n=225, and q=0.5 p=.5. Substitute these values into the formula for the test statistic z and simplify. D. P-value? Look up number from part C on the values chart to find P. E. Critical value? Find 0.05 in the numbers.
Claim: At most 20% of Internet users pay bills online. A recent survey of 395 Internet users indicated that 19% pay their bills online. a. Express the original claim in symbolic form. b. Identify the null and the alternative hypotheses.
a. p ≤ 0.2 b. H0: p=0.2 H1: p > 0.2
