FINAL EXAM (Updated version)

Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a black card and then selecting a red card. (Round to *three* decimal places.) The probability of selecting a black card and then selecting a red card is *___*.

Correct Answer: *.255* (*3.2.19*)

A probability experiment consists of rolling a fair 8​-sided die. Find the probability of the event below (type answer as either an *integer*, or a *decimal* rounded to *three* decimal places). *rolling a number divisible by 2* The probability is *_*.

Correct Answer: *.5* (*3.1.45*)

What are the two main branches of​ statistics? The two main branches of statistics are *_____________________________________________.*

Correct Answer(s): *descriptive statistics and inferential statistics.* (*1.1.4*)

Find the critical value *z*∨*c* necessary to form a confidence interval at the level of confidence shown below. (Round answer to *two* decimal places.) *"c" = 0.87* *z*∨*c* = *___*

Correct Answer: *1.51* (*6.1.5*)

A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans. A.) (0.176, 0.274) B.) (0.184, 0.266) C.) (0.167, 0.283) D.) (0.161, 0.289)

Correct Answer: B.) (0.184, 0.266) (*6.3-6*)

The region of a country with the highest level of coal production for the past six years is shown below. *Western Eastern Northern Northern Western Northern* Determine whether the data are qualitative or quantitative and identify the data​ set's level of measurement. *Part 1:* Are the data qualitative or​ quantitative? A.) Qualitative B.) Quantitative *Part 2:* What is the data​ set's level of​ measurement? A.) Nominal B.) Interval C.) Ratio D.) Ordinal

Correct Answers: *Part 1:* A.) Qualitative *Part 2:* A.) Nominal (*1.2.27*)

For each of the scatter plots​ below, determine whether there is a perfect positive linear​ correlation, a strong positive linear​ correlation, a perfect negative linear​ correlation, a strong negative linear​ correlation, or no linear correlation between the variables. Drag each of the scatter plots given above into the appropriate area below. *perfect positive linear correlation* *strong positive linear correlation* *perfect negative linear correlation* *strong negative linear correlation* *no linear correlation*

See *FINAL EXAM* slideshow. (slide *#2*.) (*9.1.9-12*)

Assume the random variable x is normally distributed with mean μ = 82 and standard deviation σ = 5. Find the indicated probability (round answer to *four* decimal places). *​P(x < 77)* ​P(x < 77) = *____*

Correct Answer: *.1587* (*5.2.1*)

About 76% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 71%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to *√((p × q)/n)*. The probability that the sample proportion surviving for at least 3 years will be less than 71% is *____*. (Round answer to *four* decimal places.)

Correct Answer: *.1635* (*5.4.41*)

Use the frequency distribution to the right, which shows the number of voters (in millions) according to​ age, to find the probability that a voter chosen at random is in the given age range. (Round answer to *three* decimal places.) *not between 21 to 24 years old* *Ages of voters* = *Frequency* *18 to 20* = *7.8* *21 to 24* = *11.6* *25 to 34* = *24.8* *35 to 44* = *26.8* *45 to 64* = *51.9* *65 and over* = *25.2* The probability is *___*.

Correct Answer: *.922* (*3.1.61*)

Use the standard normal table to find the​ z-score that corresponds to the given percentile (round answer to *three* decimal places). If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score. *P₉₅* *(I didn't copy the Standard Normal Tables because they're too big.)* The​ z-score that corresponds to P₉₅ is *____*.

Correct Answer: *1.645* (*5.3.11*)

Find the critical value *t*∨*c* for the confidence level c = 0.99 and sample size n = 23. (Round answer to the *nearest thousandth* (*three* decimal places).) *(I didn't copy the accompanying "t" - Distribution Table because it's too big.)* *t*∨*c* = *____*

Correct Answer: *2.819* (*6.2.1*)

Consider a frequency distribution of scores on a 80-point test where a few students scored much lower than the majority of students. Match this distribution with one of the graphs shown below. (Since I don't have Quizlet+, I can't insert the images of the actual frequency distributions; ergo, I pasted their descriptions.) *(A):* frequency distribution titled *A* has a horizontal axis labeled from *70 to 87.5* in increments of *2.5*, and a vertical axis labeled from *0 to 16* in increments of *1*. The frequency distribution contains eight vertical bars. The *4th bar* is labeled *77.5*, and the *8th bar* is labeled *87.5*. From left to right, the heights of the vertical bars are listed as follows, where the *location* is listed *first*, and the *height* is listed *second*: *(1, 2); (2, 3); (3, 4); (4, 5); (5, 7); (6, 13); (7, 17); (8, 14)*. *(B):* frequency distribution titled *B* has a horizontal axis labeled from *1 to 12* in increments of *1*, and a vertical axis labeled from *0 to 22* in increments of *1*. The frequency distribution contains twelve vertical bars. The *1st bar* is labeled *1*, the *4th bar* is labeled *4*, the *7th bar* is labeled *7*, and the *10th bar* is labeled *10*. From left to right, the heights of the vertical bars are listed as follows, where the *location* is listed *first*, and the *height* is listed *second*: *(1, 17); (2, 18); (3, 17); (4, 15); (5, 16); (6, 15); (7, 18); (8, 17); (9, 16); (10, 17); (11, 18); (12, 17)*. *(C):* frequency distribution titled *C* has a horizontal axis labeled from *85 to 155* in increments of *10*, and a vertical axis labeled from *0 to 15* in increments of *1*. The frequency distribution contains eight vertical bars. The *1st bar* is labeled *85*, the *4th bar* is labeled *115*, and the *7th bar* is labeled *145*. From left to right, the heights of the vertical bars are listed as follows, where the *location* is listed *first*, and the *height* is listed *second*: *(1, 3); (2, 5); (3, 13); (4, 16); (5, 15); (6, 13); (7, 5); (8, 4)*. *(D):* frequency distribution titled *D* has a horizontal axis labeled from *25,000 to 95,000* in increments of *8,750*, and a vertical axis labeled from *0 to 22* in increments of *1*. The frequency distribution contains eight vertical bars. The *1st bar* is labeled *25,000*, and the *8th bar* is labeled *95,000*. From left to right, the heights of the vertical bars are listed as follows, where the *location* is listed *first*, and the *height* is listed *second*: *(1, 22); (2, 17); (3, 9); (4, 6); (5, 4); (6, 4); (7, 3); (8, 2)*. The correct histogram is *_*. (Type either *A*, *B*, *C*, or *D* as the answer.)

Correct Answer: *A* (*2.3.15*)

How is a sample related to a​ population? Choose the correct answer below. A.) A sample is a numerical measure that describes a sample characteristic. B.) A sample is the collection of all​ outcomes, responses,​ measurements, or counts. C.) A sample is a subset of a population.

Correct Answer: C.) A sample is a subset of a population. (*1.1.1*)

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer. (Since I don't have Quizlet+, I can't insert the image of the actual histogram; ergo, I pasted the description.) A histogram has a horizontal axis labeled from *0 to 13* in increments of *1*, and a vertical axis labeled from *0 to 18* in increments of *3*. The histogram has vertical bars of width 1, where each vertical bar is centered over a horizontal axis tick mark. The heights of the vertical bars are as follows, where the *horizontal center of the bar* is listed *first*, and the *height* is listed *second*: *(1, 14); (2, 15); (3, 13); (4, 14); (5, 15); (6, 13); (7, 14); (8, 14); (9, 15); (10, 15); (11, 14); (12, 15)*. Choose the correct answer below. A.) The shape of the distribution is approximately skewed left because the bars have a tail to the left. B.) The shape of the distribution is approximately symmetric because the bars have a tail to the left and to the right. C.) The shape of the distribution is approximately uniform because the bars are approximately the same height. D.) The shape of the distribution is approximately skewed right because the bars have a tail to the right. E.) The shape of the distribution is none of these because the bars do not show any of these general trends.

Correct Answer: C.) The shape of the distribution is approximately uniform because the bars are approximately the same height. (*2.3.11*)

The expected value of an accountant's profit and loss analysis is 0. Explain what this means. Choose the correct answer below. A.) Since the expected value cannot be less than​ 0, an expected value of 0 means that the average money gained is equal to or less than the average money spent. B.) An expected value of 0 means that there was not any money gained or spent. C.) An expected value cannot be equal to 0. D.) An expected value of 0 means that the average money gained is equal to the average money spent, representing the​ break-even point.

Correct Answer: D.) An expected value of 0 means that the average money gained is equal to the average money spent, representing the​ break-even point. (*4.1.35*)

Determine if the survey question is biased. If the question is​ biased, suggest a better wording. *How much do you sleep per night during an average week​?* Is the question​ biased? A.) Yes, because it does not lead the respondent to any particular answer. A better question would be​ "Why is sleeping 8 hours per night good for​ you?" B.) Yes, because it influences the respondent into thinking that eating cake is bad for you. A better question would be​ "Do you think that sleeping 8 hours per night is good for​ you?" C.) No, because it influences the respondent into thinking that sleeping 8 hours per night is good for you. D.) No, because it does not lead the respondent to any particular answer.

Correct Answer: D.) No, because it does not lead the respondent to any particular answer. (*1.3.33*)

The frequency distribution to the right shows the number of voters​ (in millions) according to age. Consider the event below. Can it be considered​ unusual? *A voter chosen at random is between 21 and 24 years old* *Ages of voters* = *Frequency* *18 to 20* = *9.1* *21 to 24* = *5.7* *25 to 34* = *20.6* *35 to 44* = *22.5* *45 to 64* = *16.9* *65 and over* = *65.5* Choose the correct answer below. A.) Yes. The probability of the event is close to 1. B.) No. The probability of the event is not close to 0. C.) No. The probability of the event is not close to 1. D.) Yes. The probability of the event is close to 0.

Correct Answer: D.) Yes. The probability of the event is close to 0. INcorrect Answer: B.) No. The probability of the event is not close to 0. (*3.1.79*)

Use the​ box-and-whisker plot to determine if the shape of the distribution represented is​ symmetric, skewed​ left, skewed​ right, or none of these. (Since I don't have Quizlet+, I can't insert the image of the actual box-and-whisker plot; ergo, I pasted the description.) A box-and-whisker plot has a horizontal axis labeled from *0 to 200* in *increments of "20"*. Vertical line segments are drawn at the following values: *30, 60*, and *110*. A box encloses the vertical line segments at *30, 60*, and *110*, and horizontal line segments extend outward from both sides of the box to points plotted at *20* and *200*. All values are approximate. Choose the correct answer below. A.) skewed left B.) symmetric C.) none of these D.) skewed right

Correct Answer: D.) skewed right (*2.5.19*)

Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. Sample​ Space: Movies *Blue* bubble (A): Movies that are rated PG *Pink* bubble (B): Movies that receive mostly positive reviews *Purple* overlap: (A) and (B) The events *____(1)____* mutually​ exclusive, since there are *__(2)__* movies that are rated PG and *____________(3)____________*.

Correct Answers: *(1):* *are not* *(2):* *some* *(3):* *receive mostly positive reviews.* (*3.3.8*)

Determine whether the study is an observational study or an experiment. Explain. *In a survey of 1,484 adults in a​ country, 56% said the​ country's leader should release all medical information that might affect their ability to serve.* The study is *_____(1)_____,* because it *__________(2)__________* a treatment to the adults.

Correct Answers: *(1):* *observational,* *(2):* *does not apply* (*1.3.11*)

A frequency distribution is shown below. Complete parts a (1) and b (2 & 3). *The number of televisions per household in a small town* *Televisions (x)* = *Households (P(x))* *0* = *28* *1* = *442* *2* = *723* *3* = *1,410* *Part 1 (a):* Use the frequency distribution to construct a probability distribution (round answers to *three* decimal places). *x* = *​P(x)* 0 = *__(1)__* 1 = *_(2)_* 2 = *__(3)__* 3 = *__(4)__* *Part 2 ​(b):* Graph the probability distribution using a histogram. Choose the correct graph of the distribution below (since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I pasted their descriptions). A.) A histogram has a horizontal x-axis labeled *"# of Televisions"* from *0 to 3* in increments of *1*, and a vertical *P(x)-axis* labeled from *0 to 0.6* in increments of *0.1*. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of televisions* is listed *first*, and the *approximate height* is listed *second*: *(0, 0.01); (1, 0.17); (2, 0.28); (3, 0.54)*. B.) A histogram has a horizontal x-axis labeled *"# of Televisions"* from *0 to 3* in increments of *1*, and a vertical *P(x)-axis* labeled from *0 to 0.6* in increments of *0.1*. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of televisions* is listed *first*, and the *approximate height* is listed *second*: *(0, 0.01); (1, 0.28); (2, 0.54); (3, 0.17)*. C.) A histogram has a horizontal x-axis labeled *"# of Televisions"* from *0 to 3* in increments of *1*, and a vertical *P(x)-axis* labeled from *0 to 0.6* in increments of *0.1*. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of televisions* is listed *first*, and the *approximate height* is listed *second*: *(0, 0.54); (1, 0.28); (2, 0.17); (3, 0.01)*. *Part 3 (b):* Describe the​ histogram's shape. Choose the correct answer below. A.) skewed left B.) symmetric C.) skewed right

Correct Answers: *Part 1 (a):* *(1):* *.011* *(2):* *.17* *(3):* *0.278* *(4):* *.542* *Part 2 (b):* A.) A histogram has a horizontal x-axis labeled *"# of Televisions"* from *0 to 3* in increments of *1*, and a vertical *P(x)-axis* labeled from *0 to 0.6* in increments of *0.1*. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of televisions* is listed *first*, and the *approximate height* is listed *second*: *(0, 0.01); (1, 0.17); (2, 0.28); (3, 0.54)*. *Part 3 (b):* A.) skewed left INcorrect Answer(s): *Part 1 (a):* *(3)*: *.281* (*4.1.19-T*)

The data show the number of vacation days used by a sample of 20 employees in a recent year. Use technology to answer parts 1 (a) and 2 (b). *Part 1 (a):* Find the data​ set's first,​ second, and third quartiles. *Part 2 (b):* Draw a​ box-and-whisker plot that represents the data set. *1 4 2 3 9 7 1 8 10 2 5 6 0 9 6 2 3 6 1 3* *Part 1 (a):* Find the three quartiles. (Type answers as either *integers* or *decimals*, but *DO NOT ROUND*.) *(1):* Q₁ = *_* *(2):* Q₂ = *__* *(3):* Q₃ = *__* *Part 2 (b):* Choose the correct answer plot below. Note that different technologies will produce slightly different results. (Since I don't have Quizlet+, I can't insert the images of the actual box-and-whisker plots; ergo, I pasted their descriptions.) A.) A box-and-whisker plot has a horizontal axis labeled from *0 to 10* in *increments of "1"*. Vertical line segments are drawn at the following values: *0, 2, 3.5, 6.5*, and *10*. A box encloses the vertical line segments at *2, 3.5*, and *6.5*, and horizontal line segments extend outward from both sides of the box to the vertical line segments at *0* and *10*. B.) A box-and-whisker plot has a horizontal axis labeled from *0 to 10* in *increments of "1"*. Vertical line segments are drawn at the following values: *0, 3.5, 6.5, 8*, and *10*. A box encloses the vertical line segments at *3.5, 6.5*, and *8*, and horizontal line segments extend outward from both sides of the box to the vertical line segments at *0* and *10*. C.) A box-and-whisker plot has a horizontal axis labeled from *0 to 10* in *increments of "1"*. Vertical line segments are drawn at the following values: *0, 1, 3, 3.5*, and *10* . A box encloses the vertical line segments at *1* and *3*, and horizontal line segments extend outward from both sides of the box to the vertical line segments at *0* and *10*.

Correct Answers: *Part 1 (a):* *(1):* *2* *(2):* *3.5* *(3):* *6.5* *Part 2 (b):* A.) A box-and-whisker plot has a horizontal axis labeled from *0 to 10* in *increments of "1"*. Vertical line segments are drawn at the following values: *0, 2, 3.5, 6.5*, and *10*. A box encloses the vertical line segments at *2, 3.5*, and *6.5*, and horizontal line segments extend outward from both sides of the box to the vertical line segments at *0* and *10*. (*2.5.24-T*)

You roll a​ six-sided die. Find the probability of each of the following scenarios. (Round all answers to *three* decimal places). ​*Part 1 (a):* Rolling a 4 or a number greater than 3 *Part 2 ​(b):* Rolling a number less than 4 or an even number *Part 3 ​(c):* Rolling a 2 or an odd number *Part 1 ​(a):* ​P(4 or number > 3) = *_* *Part 2 ​(b):* P(1 or 2 or 3 or 4 or ​6) = *___* *Part 3 ​(c):* ​P(2 or 1 or 3 or​ 5) = *___*

Correct Answers: *Part 1 (a):* *.5* *Part 2 (b):* *.833* *Part 3 (c):* *.667* (*3.3.18*)

The accompanying table shows the numbers of male and female students in a particular country who received​ bachelor's degrees in business in a recent year. Complete parts​ 1 (a) and 2 (b) below. (Since I don't have Quizlet+, I can't insert the image of the table; ergo, I took a screenshot of it and put it in the *FINAL EXAM* slideshow. (slide *#4*).) *Part 1 (a):* Find the probability that a randomly selected student is *male*​, *"given"* that the student received a *business degree*. (Round to *three* decimal places.) The probability that a randomly selected student is​ male, given that the student received a business​ degree, is *___*. *Part 2 (b):* Find the probability that a randomly selected student received a *business​ degree*, *"given"* that the student is *female*. (Round to *three* decimal places.) The probability that a randomly selected student received a business​ degree, given that the student is​ female, is *____*.

Correct Answers: *Part 1 (a):* *.527* *Part 2 (b):* *0.161* INcorrect Answer(s): *Part 2 (b):* *.156* (*3.2.7*)

The depths​ (in inches) at which 10 artifacts are found are listed. Complete parts 1 (a) and 2 (b) below (round both answers to the *nearest tenth* (*one* decimal place).) *37.6 24.7 31.8 26.7 45.1 34.2 30.2 29.9 30.8 23.4* *Part 1 (a):* Find the range of the data set. Range = *___* *Part 2 (b):* Change 45.1 to 50.6 and find the range of the new data set. Range = *___*

Correct Answers: *Part 1 (a):* *21.7* *Part 2 (b):* *27.2* (*2.4.11*)

The percent of college​ students' marijuana use for a sample of 96,128 students is shown in the accompanying pie chart. Find the probability of each event listed in parts​ 1 (a) through​ 4 (d) below (round all answers to *one* decimal place). (Since I don't have Quizlet+, I can't insert the image of the actual pie chart (circle graph); ergo, I pasted the description.) A circle graph entitled *"Marijuana Use in the Last 30 Days"* is divided into five sectors with labels and approximate sizes as a percentage of a circle as follows: *Never used, 57.3%; Used, but not in the last 30 days, 24.0%; Used 1 - 9 days, 12.0%; Used 10 - 29 days, 5.0%; Used all 30 days, 1.7%*. *Part 1 (a):* Randomly selecting a student who never used marijuana The probability is *___%*. *Part 2 (b):* Randomly selecting a student who used marijuana The probability is *___%*. *Part 3 (c):* Randomly selecting a student who used marijuana between 1 and 29 of the last 30 days The probability is *__%*. *Part 4 (d):* Randomly selecting a student who used marijuana on at least 1 of the last 30 days The probability is *___%*.

Correct Answers: *Part 1 (a):* *57.3%* *Part 2 (b):* *42.7%* *Part 3 (c):* *17%* *Part 4 (d):* *18.7%* (*3.3.20*)

A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 919 milligrams. A random sample of 46 breakfast sandwiches has a mean sodium content of 913 milligrams. Assume the population standard deviation is 18 milligrams. At *α* = 0.10, do you have enough evidence to reject the​ restaurant's claim? Complete parts 1 (a) through 5 (d & e). *Part 1 (a):* Identify the claim and state the null and alternative hypothesis. A.) *H₀*: μ ≤ 913 *H*∨*a*: μ < 913 (claim) B.) *H₀*: μ ≤ 919 (claim) *H*∨*a*: μ > 919 C.) *H₀*: μ < 913 (claim) *H*∨*a*: μ ≥ 913 D.) *H₀*: μ > 919 *H*∨*a*: μ ≤ 919 (claim) E.) *H₀*: μ ≠ 919 (claim) *H*∨*a*: μ = 919 F.) *H₀*: μ = 913 (claim) *H*∨*a*: μ ≠ 913 *Part 2 (b):* Identify the critical value(s). Use technology. (Round answer(s) to *two* decimal places, and use a *comma* to separate answers (if needed).) *z₀* = *___* *Part 3 (b):* Identify the rejection​ region(s). Select the correct choice below. A.) The rejection region is *z* > 1.28. B.) The rejection region is *z* < 1.28. C.) The rejection regions are *z* > 1.28 and *z* < -1.28. *Part 4 (c):* Identify the standardized test statistic. Use technology. (Round answer to *two* decimal places.) *z* = *___* ​ *(Part 5 (d)):* Decide whether to reject or fail to reject the null hypothesis and *(Part 5 (e)):* interpret the decision in the context of the original claim. A.) Fail to reject *H₀*. There is not sufficient evidence to reject the claim that the mean sodium content is no more 919 milligrams. B.) Reject *H₀*. There is not sufficient evidence to reject the claim that the mean sodium content is no more 919 milligrams. C.) Reject *H₀*. There is sufficient evidence to reject the claim that the mean sodium content is no more 919 milligrams. D.) Fail to reject *H₀*. There is sufficient evidence to reject the claim that the mean sodium content is no more 919 milligrams.

Correct Answers: *Part 1 (a):* B.) *H₀*: μ ≤ 919 (claim) *H*∨*a*: μ > 919 *Part 2 (b):* *1.28* *Part 3 (b):* A.) The rejection region is *z* > 1.28. *Part 4 (c):* *-2.26* *Part 5 (d & e):* A.) Fail to reject *H₀*. There is not sufficient evidence to reject the claim that the mean sodium content is no more 919 milligrams. (*7.2.39-T*)

A medical researcher says that less than 87% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that​ country, 85% think that healthy children should be required to be vaccinated. At *α* = 0.01, is there enough evidence to support the​ researcher's claim? Complete parts 1 & 2 (a) through 6 (d & e) below. *(a):* Identify the claim and state *H₀* and *H*∨*a*. *Part 1 (a):* Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type answer(s) as either *integers* or *decimals*, but *DO NOT ROUND*.) A.) *__%* of adults in the country think that healthy children should be required to be vaccinated. B.) Less than *__%* of adults in the country think that healthy children should be required to be vaccinated. C.) More than *__%* of adults in the country think that healthy children should be required to be vaccinated. D.) The percentage of adults in the country who think that healthy children should be required to be vaccinated is not *__%*. *Part 2 (a):* Let *p* be the population proportion of​ successes, where a success is an adult in the country who thinks that healthy children should be required to be vaccinated. State *H₀* and *H*∨*a*. Select the correct choice below and fill in the answer boxes to complete your choice. (Round answers to *two* decimal places.) A.) *H₀*: p < *__* *H*∨*a*: p ≥ *__* B.) *H₀*: p ≤ *__* *H*∨*a*: p > *__* C.) *H₀*: p ≥ *__* *H*∨*a*: p < *__* D.) *H₀*: p ≠ *__* *H*∨*a*: p = *__* E.) *H₀*: p > *__* *H*∨*a*: p ≤ *__* F.) *H₀*: p = *__* *H*∨*a*: p ≠ *__* *(b):* Find the critical value(s) and identify the rejection region(s). *Part 3 (b):* Identify the critical value(s) for this test. (Round answer(s) to *two* decimal places, and use a *comma* to separate answers (if needed).) *z₀* = *___* *Part 4 (b):* Identify the rejection region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice. (Round answer(s) to *two* decimal places.) A.) The rejection region is z < *___*. B.) The rejection region is z > *___*. C.) The rejection region is *___* < z < *___*. D.) The rejection regions are z < *___* and z > *___*. *Part 5 (c):* Find the standardized test statistic, *z*. (Round answer to *two* decimal places.) *z* = *___* *(Part 6 (d)):* Decide whether to *reject* or *fail to reject* the null hypothesis, and *(Part 6 (e)):* interpret the decision in the context of the original claim. *_______(1)_______* the null hypothesis. There *___(2)___* enough evidence to *____(3)____* the​ researcher's claim.

Correct Answers: *Part 1 (a):* B.) Less than *87%* of adults in the country think that healthy children should be required to be vaccinated. *Part 2 (a):* C.) *H₀*: p ≥ *.87* *H*∨*a*: p < *.87* *Part 3 (b):* *-2.33* *Part 4 (b):* A.) The rejection region is z < *-2.33*. *Part 5 (c):* *-.94* *Part 6 (d & e):* *(1):* *Fail to reject* *(2):* *is not* *(3):* *support* (*7.4.7-T*)

Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns. *Number of​ classes:* *8* *Data​ set:* *Reaction time (in milliseconds) of 30 adult females to an auditory stimulus* *427 293 383 338 514 423 385 430 373 310 442 386 354 471 385 412 440 427 304 455 310 307 325 410 450 387 320 357 507 415* *Part 1:* Construct a frequency distribution of the data. Use the minimum data entry as the lower limit of the first class. *Class (I)* *Frequency (II)* 1.) *I:* *___* - *___* *II:* *_* 2.) *I:* *___* - *___* *II:* *_* 3.) *I:* *___* - *___* *II:* *_* 4.) *I:* *___* - *___* *II:* *_* 5.) *I:* *___* - *___* *II:* *_* 6.) *I:* *___* - *___* *II:* *_* 7.) *I:* *___* - *___* *II:* *_* 8.) *I:* *___* - *___* *II:* *_* *Part 2:* Construct a frequency histogram of the data. (Since I don't have Quizlet+, I can't insert the images of the actual frequency histograms; ergo, I pasted their descriptions.) A.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in increments of *1*, and a vertical axis labeled *"Frequency"* from *0 to 10* in increments of *1*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(1, 6); (2, 2); (3, 3); (4, 5); (5, 7); (6, 4); (7, 1); (8, 2)*. B.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in increments of *1*, and a vertical axis labeled *"Frequency"* from *0 to 10* in increments of *1*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(1, 1); (2, 6); (3, 3); (4, 7); (5, 4); (6, 2); (7, 2); (8, 5)*. C.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in increments of *1*, and a vertical axis labeled *"Frequency"* from *0 to 10* in increments of *1*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(1, 2); (2, 1); (3, 4); (4, 7); (5, 5); (6, 3); (7, 2); (8, 6)*. D.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in increments of *1*, and a vertical axis labeled *"Frequency"* from *0 to 10* in increments of *1*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(1, 2); (2, 6); (3, 5); (4, 3); (5, 4); (6, 7); (7, 2); (8, 1)*. *Part 3:* Describe any patterns. Choose the correct answer below. A.) The class with the greatest frequency is class 8. The class with the least frequency is class 2. B.) The class with the greatest frequency is class 7. The class with the least frequency is class 5. C.) The class with the greatest frequency is class 5. The class with the least frequency is class 7. D.) The class with the greatest frequency is class 1. The class with the least frequency is class 8.

Correct Answers: *Part 1* (*I*; *II*): 1.) *295* - *322*; *6* 2.) *323* - *350*; *2* 3.) *351* - *378*; *3* 4.) *379* - *406*; *5* 5.) *407* - *434*; *7* 6.) *435* - *462*; *4* 7.) *463* - *490*; *1* 8.) *491* - *518*; *2* *Part 2:* A.) A frequency histogram has a horizontal axis labeled *"Class"* from *1 to 8* in increments of *1*, and a vertical axis labeled *"Frequency"* from *0 to 10* in increments of *1*. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the *horizontal axis label* is listed *first*, and the *height* is listed *second*: *(1, 6); (2, 2); (3, 3); (4, 5); (5, 7); (6, 4); (7, 1); (8, 2)*. *Part 3:* C.) The class with the greatest frequency is class 5. The class with the least frequency is class 7. (*2.1.33*)

The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately​ bell-shaped. Compare the​ z-scores for the actors in the following situation. *Best Actor:* *μ = 45.0* *σ = 6.3* *Best Supporting Actor:* *μ = 49.0* *σ = 15* *In a particular​ year, the Best Actor was 51 years old and the Best Supporting Actor was 45 years old.* *Part 1:* Determine the​ z-scores for each. (Round answers to *two* decimal places.) *(1):* Best Actor: z = *__* *(2):* Best Supporting Actor: z = *__* *Part 2:* Interpret the​ z-scores. The Best Actor was *____________(1)____________* the​ mean, and the Best Supporting Actor was *__________(2)__________* the mean. *___(3)___* of their ages​ is/are unusual.

Correct Answers: *Part 1:* *(1):* *.95* *(2):* *-.27* *Part 2:* *(1):* *about 1 standard deviation above* *(2):* *less than 1 standard deviation below* *(3):* *Neither* (*2.5.51*)

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (The pair of variables have a significant​ correlation.) Then use the regression equation to predict the value of *y* for each of the given *x* - values, if meaningful. The number of hours 6 students spent studying for a test and their scores on that test are shown below. *Hours spent studying (x)* = *Test score (y)* *1* = *40* *1* = *45* *3* = *52* *3* = *49* *4* = *63* *6* = *70* *Part 3 (a): x = 2 hours* *Part 4 (b): x = 2.5 hours* *Part 5 (c): x = 14 hours* *Part 6 (d): x = 1.5 hours* *Part 1:* Find the regression equation. (Round the *slope (1)* to *three* decimal places, and round the *"y" - intercept (2)* to *two* decimal places.) *ŷ* = *__(1)__*x + (*_(2)_*) *Part 2:* Choose the correct graph below. (Since I don't have Quizlet+, I can't insert the images of the actual scatter plots; ergo, I pasted their descriptions.) A.) A scatter plot has a horizontal axis labeled *Hours studying* from *0 to 8* in increments of *1*, and a vertical axis labeled *Test score* from *0 to 80* in increments of *10*. The following *6* points are plotted (*Hours studying*, *Test score*): *(5, 39), (3, 44), (4, 51), (2, 49), (2, 60), (2, 60)*. A trend line that *falls* from left to right passes through the points *(2, 55)* and *(6, 32)*. All coordinates are approximate. B.) A scatter plot has a horizontal axis labeled *Hours studying* from *0 to 8* in increments of *1*, and a vertical axis labeled *Test score* from *0 to 80* in increments of *10*. The following *6* points are plotted (*Hours studying*, *Test score*): *(4, 38), (3, 44), (1, 51), (1, 48), (2, 62), (4, 69)*. A trend line that *falls* from left to right passes through the points *(2, 40)* and *(6, 17)*. All coordinates are approximate. C.) A scatter plot has a horizontal axis labeled *Hours studying* from *0 to 8* in increments of *1*, and a vertical axis labeled *Test score* from *0 to 80* in increments of *10*. The following *6* points are plotted (*Hours studying*, *Test score*): *(1, 40), (1, 45), (3, 52), (3, 49), (4, 63), (6, 70)*. A trend line that *rises* from left to right passes through the points *(2, 47)* and *(6, 70)*. All coordinates are approximate. D.) A scatter plot has a horizontal axis labeled *Hours studying* from *0 to 8* in increments of *1*, and a vertical axis labeled *Test score* from *0 to 80* in increments of *10*. The following *6* points are plotted (*Hours studying*, *Test score*): *(2, 43), (2, 50), (4, 59), (4, 54), (5, 68), (7, 75)*. A trend line that *rises* from left to right passes through the points *(2, 53)* and *(6, 76)*. All coordinates are approximate. *Part 3 (a):* Predict the value of *y* for *x = 2*. Choose the correct answer below. A.) 44.6 B.) 50.3 C.) 47.4 D.) not meaningful *Part 4 (b):* Predict the value of *y* for *x = 2.5*. Choose the correct answer below. A.) 50.3 B.) 116.1 C.) 44.6 D.) not meaningful *Part 5 (c):* Predict the value of *y* for *x = 14*. Choose the correct answer below. A.) 47.4 B.) 50.3 C.) 116.1 D.) not meaningful *Part 6 (d):* Predict the value of *y* for *x = 1.5*. Choose the correct answer below. A.) 116.1 B.) 44.6 C.) 47.4 D.) not meaningful

Correct Answers: *Part 1:* *(1):* *5.722* *(2):* *36* *Part 2:* C.) A scatter plot has a horizontal axis labeled *Hours studying* from *0 to 8* in increments of *1*, and a vertical axis labeled *Test score* from *0 to 80* in increments of *10*. The following *6* points are plotted (*Hours studying*, *Test score*): *(1, 40), (1, 45), (3, 52), (3, 49), (4, 63), (6, 70)*. A trend line that *rises* from left to right passes through the points *(2, 47)* and *(6, 70)*. All coordinates are approximate. *Part 3 (a):* C.) 47.4 *Part 4 (b):* A.) 50.3 *Part 5 (c):* D.) not meaningful *Part 6 (d):* B.) 44.6 (*9.2.19-T*)

The number of hospital beds in a sample of 20 hospitals is shown below. Construct a frequency distribution and a frequency histogram for the data set using 5 classes. Describe the shape of the histogram as​ symmetric, uniform, negatively​ skewed, positively​ skewed, or none of these. *169 167 126 126 175 159 163 224 141 141 192 209 150 249 267 245 296 141 202 176* *Part 1:* Construct a frequency distribution for the data set using 5 classes. (Type answers as *whole numbers* (*zero* decimal places).) Class = *Frequency ("1" - "5")* 126-160 = *_(1)_* 161-195 = *_(2)_* 196-230 = *_(3)_* 231-265 = *_(4)_* 266-300 = *_(5)_* *Part 2:* Construct a frequency histogram for the data set using the frequency distribution. Choose the correct answer below. (Since I don't have Quizlet+, I can't insert the images of the actual histograms; ergo, I pasted their descriptions.) A.) A histogram titled *"Hospital Beds"* has a horizontal axis labeled *"Number of beds"* from *108 to 318* in increments of *35*, and a vertical axis labeled *"Frequency"* from *0 to 8* in increments of *1*. The histogram contains 5 vertical bars of width 35 centered over horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of beds* is listed *first*, and the *height* is listed *second*: *(143, 7); (178, 3); (213, 2); (248, 2); (283, 6)*. B.) A histogram titled *"Hospital Beds"* has a horizontal axis labeled *"Number of beds"* from *108 to 318* in increments of *35*, and a vertical axis labeled *"Frequency"* from *0 to 8* in increments of *1*. The histogram contains 5 vertical bars of width 35 centered over horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of beds* is listed *first*, and the *height* is listed *second*: *(143, 2); (178, 2); (213, 3); (248, 6); (283, 7)*. C.) A histogram titled *"Hospital Beds"* has a horizontal axis labeled *"Number of beds"* from *108 to 318* in increments of *35*, and a vertical axis labeled *"Frequency"* from *0 to 8* in increments of *1*. The histogram contains 5 vertical bars of width 35 centered over horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of beds* is listed *first*, and the *height* is listed *second*: *(143, 7); (178, 6); (213, 3); (248, 2); (283, 2)*. D.) A histogram titled *"Hospital Beds"* has a horizontal axis labeled *"Number of beds"* from *108 to 318* in increments of *35*, and a vertical axis labeled *"Frequency"* from *0 to 8* in increments of *1*. The histogram contains 5 vertical bars of width 35 centered over horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of beds* is listed *first*, and the *height* is listed *second*: *(143, 3); (178, 7); (213, 6); (248, 2); (283, 2)*. *Part 3:* Describe the shape of the histogram as​ symmetric, uniform, negatively​ skewed, positively​ skewed, or none of these. Choose the correct answer below. A.) The histogram is negatively skewed because the left tail is longer than the right tail. B.) The histogram is positively skewed because the right tail is longer than the left tail. C.) The histogram is uniform because the classes all have approximately the same height. D.) The histogram is​ symmetric, but not​ uniform, because the two halves are approximately mirror images. E.) The histogram has none of these shapes.

Correct Answers: *Part 1:* *(1):* *7* *(2):* *6* *(3):* *3* *(4):* *2* *(5):* *2* *Part 2:* C.) A histogram titled *"Hospital Beds"* has a horizontal axis labeled *"Number of beds"* from *108 to 318* in increments of *35*, and a vertical axis labeled *"Frequency"* from *0 to 8* in increments of *1*. The histogram contains 5 vertical bars of width 35 centered over horizontal axis tick marks. The heights of the vertical bars are as follows, where the *number of beds* is listed *first*, and the *height* is listed *second*: *(143, 7); (178, 6); (213, 3); (248, 2); (283, 2)*. *Part 3:* B.) The histogram is positively skewed because the right tail is longer than the left tail. (*2.3.53*)

The ages of the winners of a cycling tournament are approximately​ bell-shaped. The mean age is 28.8 ​years, with a standard deviation of 3.8 years. The winner in one recent year was 31 years old. ​ *Part 1 (a):* Transform the age to a​ z-score. *Part 2 ​(b):* Interpret the results. *Part 3 ​(c):* Determine whether the age is unusual. *Part 1 (a):* Transform the age to a​ z-score. (Type answer as either an *integer* or a *decimal* (rounded to *two* decimal places).) z = *__* *Part 2 (b):* Interpret the results. (Type answer as either an *integer* or a *decimal* (rounded to *two* decimal places).) An age of 31 is *_(1)_* standard​ deviation(s) *___(2)___* the mean. *Part 3 (c):* Determine whether the age is unusual. Choose the correct answer below. A.) No, this value is not unusual. A z-score outside of the range from −2 and 2 is not unusual. B.) No, this value is not unusual. A z-score between −2 to 2 is not unusual. C.) Yes, this value is unusual. A z-score outside of the range from −2 to 2 is unusual. D.) Yes, this value is unusual. A z-score between −2 and 2 is unusual.

Correct Answers: *Part 1:* *.58* *Part 2:* *(1):* *.58* *(2):* *above* *Part 3:* B.) No, this value is not unusual. A z-score between −2 to 2 is not unusual. (*2.5.45*)

Use the given minimum and maximum data​ entries, and the number of​ classes, to find the class​ width, the lower class​ limits, and the upper class limits. *minimum = 9, maximum = 91, 6 classes* *Part 1:* The class width is *__*. *Part 2:* Choose the correct lower class limits below. A.) 23, 36, 51, 65, 79, 92 B.) 9, 23, 37, 51, 65, 79 C.) 9, 22, 37, 50, 64, 79 D.) 22, 36, 51, 64, 78, 92 *Part 3:* Choose the correct upper class limits below. A.) 23, 37, 50, 64, 79, 92 B.) 23, 37, 51, 65, 79, 92 C.) 22, 36, 50, 64, 78, 92 D.) 22, 36, 51, 65, 78, 92

Correct Answers: *Part 1:* *14* *Part 2:* B.) 9, 23, 37, 51, 65, 79 *Part 3:* C.) 22, 36, 50, 64, 78, 92 (*2.1.12*)

For the following​ situation, find the mean and standard deviation of the population. List all samples​ (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. (Round all answers to *two* decimal places.) *The word counts of five essays are 509, 620, 551, 610, and 578. Use a sample size of 2.* *Part 1:* The mean of the population is *____*. *Part 2:* The standard deviation of the population is *____*. *Part 3:* Identify all samples of size 2 with the correct accompanying means below. A.) 620, 610, x̄ = 615 B.) 509, 509, x̄ = 509 C.) 620, 509, x̄ = 564.5 D.) 578, 509, x̄ = 543.5 E.) 620, 551, x̄ = 585.5 F.) 620, 620, x̄ = 620 G.) 610, 578, x̄ = 594 H.) 578, 551, x̄ = 564.5 I.) 509, 551, x̄ = 585.5 J.) 578, 578, x̄ = 578 K.) 578, 620, x̄ = 599 L.) 551, 620, x̄ = 585.5 M.) 610, 509, x̄ = 559.5 N.) 610, 610, x̄ = 610 O.) 551, 610, x̄ = 580.5 P.) 509, 578, x̄ = 543.5 Q.) 610, 620, x̄ = 615 R.) 610, 620​, x̄ = 556.5 S.) 578, 634, x̄ = 606 T.) 610, 551, x̄ = 580.5 U.) 578, 610, x̄ = 594 V.) 551, 551, x̄ = 551 W.) 620, 578, x̄ = 599 X.) 551, 578, x̄ = 564.5 Y.) 509, 620, x̄ = 564.5 Z.) 509, 610, x̄ = 559.5 [.] 551, 509, x̄ = 530 *Part 4:* The mean of the sampling distribution is *_____*. *Part 5:* The standard deviation of the sampling distribution is *____*. *Part 6:* Choose the correct comparison of the population and sampling distribution below. A.) The means and standard deviations are equal. B.) The means are equal but the standard deviation of the sampling distribution is larger. C.) The means are not equal and the standard deviation of the sampling distribution is smaller. D.) The means are equal but the standard deviation of the sampling distribution is smaller. E.) The means are not equal and the standard deviation of the sampling distribution is larger.

Correct Answers: *Part 1:* *573.6* *Part 2:* *40.45* *Part 3:* A.) 620, 610, x̄ = 615 B.) 509, 509, x̄ = 509 C.) 620, 509, x̄ = 564.5 D.) 578, 509, x̄ = 543.5 E.) 620, 551, x̄ = 585.5 F.) 620, 620, x̄ = 620 G.) 610, 578, x̄ = 594 H.) 578, 551, x̄ = 564.5 I.) 509, 551, x̄ = 530 J.) 578, 578, x̄ = 578 K.) 578, 620, x̄ = 599 L.) 551, 620, x̄ = 585.5 M.) 610, 509, x̄ = 559.5 N.) 610, 610, x̄ = 610 O.) 551, 610, x̄ = 580.5 P.) 509, 578, x̄ = 543.5 Q.) 610, 620, x̄ = 615 T.) 610, 551, x̄ = 580.5 U.) 578, 610, x̄ = 594 V.) 551, 551, x̄ = 551 W.) 620, 578, x̄ = 599 X.) 551, 578, x̄ = 564.5 Y.) 509, 620, x̄ = 564.5 Z.) 509, 610, x̄ = 559.5 [.] 551, 509, x̄ = 530 *Part 4:* *573.6* *Part 5:* *28.6* *Part 6:* D.) The means are equal but the standard deviation of the sampling distribution is smaller. (*5.4.11*)

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Assume the population of interest is the student body at a university. *Questioning students as they leave an academic building​, a researcher asks 360 students about their eating habits.* *Part 1:* What type of sampling is​ used? A.) Convenience sampling is​ used, because students are chosen due to convenience of location. B.) Cluster sampling is​ used, because students are divided into​ groups, groups are chosen at​ random, and every student in one of those groups is sampled. C.) Simple random sampling is​ used, because students are chosen at random. D.) Stratified sampling is​ used, because students are divided into​ groups, and students are chosen at random from these groups. E.) Systematic sampling is​ used, because students are selected from a​ list, with a fixed interval between students on the list. *Part 2:* What potential sources of bias are​ present, if​ any? Select all that apply. A.) University students may not be representative of all people in their age group. B.) Because of the personal nature of the​ question, students may not answer honestly. C.) The sample only consists of members of the population that are easy to get. These members may not be representative of the population. D.) There are no potential sources of bias.

Correct Answers: *Part 1:* A.) Convenience sampling is​ used, because students are chosen due to convenience of location. *Part 2:* B.) Because of the personal nature of the​ question, students may not answer honestly. C.) The sample only consists of members of the population that are easy to get. These members may not be representative of the population. (*1.3.24*)

The masses (in grams) of a sample of a species of fish caught in the waters of a region are shown below. *21.5 17.2 19.9 18.6 22.1 21.1 17.4 22.1 18.9* Determine whether the data are qualitative or quantitative and identify the data​ set's level of measurement. *Part 1:* Are the data qualitative or quantitative? A.) Qualitative B.) Quantitative *Part 2:* What is the data​ set's level of​ measurement? A.) Ratio B.) Interval C.) Ordinal D.) Nominal

Correct Answers: *Part 1:* B.) Quantitative *Part 2:* A.) Ratio (*1.2.30*)

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. *Corn is planted on a 47-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.* *Part 1:* What type of sampling is​ used? A.) Simple random sampling is​ used, since each sample of corn plants of the same amount has the same chance of being selected. B.) Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot. C.) Convenience sampling is​ used, since the corn plants closest to the barn are sampled. D.) Cluster sampling is​ used, since the field is divided into subplots, a number of subplots is selected, and every corn plant in the selected subplots is sampled. *Part 2:* What potential sources of bias are​ present, if​ any? Select all that apply. A.) Certain subplots may have more or fewer corn plants than others. Samples from these subplots may bias the overall sample. B.) The sample only consists of the corn plants that are easiest to reach. This may not be representative of the entire population. C.) It is possible that, due to the sampling error, the sample will not be representative. D.) There are no potential sources of bias.

Correct Answers: *Part 1:* B.) Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot. *Part 2:* A.) Certain subplots may have more or fewer corn plants than others. Samples from these subplots may bias the overall sample. (*1.3.27*)

Use technology and a *t* - test to test the claim about the population​ mean, *μ*, at the given level of significance, *α*, using the given sample statistics. Assume the population is normally distributed. *Claim:* *μ > 74*; *α = 0.05* *Sample​ statistics:* *x̄ = 76.4*; *s = 3.3*; *n = 26* *Part 1:* What are the null and alternative hypotheses? Choose the correct answer below. A.) *H₀*: μ ≥ 74 *H*∨*a*: μ < 74 B.) *H₀*: μ = 74 *H*∨*a*: μ ≠ 74 C.) *H₀*: μ ≤ 74 *H*∨*a*: μ > 74 D.) *H₀*: μ ≠ 74 *H*∨*a*: μ = 74 *Part 2:* What is the standardized test statistic? (Round answer to *two* decimal places.) The standardized test statistic is *___*. *Part 3:* What is the *P* - value of the test statistic? (Round answer to *three* decimal places.) *P* - value = *___* *Part 4:* Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. A.) Reject *H₀*. There is not enough evidence to support the claim. B.) Fail to reject *H₀*. There is not enough evidence to support the claim. C.) Fail to reject *H₀*. There is enough evidence to support the claim. D.) Reject *H₀*. There is enough evidence to support the claim.

Correct Answers: *Part 1:* C.) *H₀*: μ ≤ 74 *H*∨*a*: μ > 74 *Part 2:* *3.71* *Part 3:* *.001* *Part 4:* D.) Reject *H₀*. There is enough evidence to support the claim. (*7.3.14-T*)

Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. *Randomly choosing a number from the odd numbers between 1 and 10, inclusive* *Part 1:* The sample space is ​{*_, _, _, _, __*​}. (Use a *comma* to separate answers (if needed), and type the answers in *ascending* order (from *least* to *greatest).) *Part 2:* There are *_* ​outcome(s) in the sample space.

Correct Answers: *Part 1:* {*2, 4, 6, 8, 10*} *Part 2:* *5* (*3.1.25*)