Math 243 Final

Heights in a certain population (in inches) are normally distributed with mean 66 and standard deviation 2.3. If a person is randomly chosen from the population, what is the probability that they are at least 70 inches tall?

0.041

The sample mean and standard deviation from a random sample of 21 observations from a normal population were computed as x¯=31 and s = 15. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 4% significance level that the population mean is greater than 27. t=

1.22

In the normal distribution N(15,3), what is the z-score corresponding to the data point 19? What data point has a z-score of -1.6?

1.33,10.2

You are testing the null hypothesis μ=15 against the alternative hypothesis μ>15, and your data is from a sample of size 37. In order to reject the null hypothesis at the 0.03 confidence level, you will need to get a t-statistic that is at least

1.94

For a normal distribution N(m,25), what percent of the data lies between m+25 and m+50? Use the 68-95-99.7 rule.

13.5

A 92% confidence interval for the mean weight, in pounds, of Oregonian bald eagles is [6.5,14.5]. What is the margin of error?

4 lbs

A certain quantitative variable has standard deviation 12 across an entire population. If you want to construct a 95% confidence interval for the mean with margin of error less than 9, what is the smallest sample size you could use?

7

Scores on an exam are normally distributed with mean 72 and standard deviation 5. What would a person have to score higher than in order to be in the top 20 percent?

76.21

In the normal distribution N(35,10), what percentage of the data has z-scores lying between -1.2 and 1.2?

76.99

Soda cans are supposed to contain 12 ounces of liquid. We believe that, on average, cans of Jolt Soda contain less than 12 ounces. We perform a statistical test to examine this claim, using 0.03 for the significance level. The power of the test is 0.89. A) The probability of making a Type I error in our test is B) The probability of making a Type II error in our test is C) A Type I error means

A) 0.03 B) 0.11 C) concluding that the average liquid in a Jolt can is less than 12 oz, when the average actually equals 12

The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.15 ounces. A) What is the probability that a randomly chosen chocolate bar has weight at least 8.3 ounces? B) What weights represent the heaviest 10% of all chocolate bars? 8.29 and above C) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with four of these chocolate bars is between 7.94 and 8.25 ounces? D) For a SRS of four of these chocolate bars, what is the levelL such that there is a 3% chance that the average weight is less than L?

A) 0.09 B) 8.29 and above C) 0.96 D) 7.96

The distribution of weights of adult males in a certain county is moderately right-skewed with a mean weight of 180 lbs and standard deviation 16 lbs. A) What is the probability that a simple random sample of 100 adult males from this county has a mean weight between 175 and 182 lbs? B) What is the probability that a simple random sample of 81 adult males from this county has a total weight exceeding 14500 lbs?

A) 0.89 B) 0.71

Test the claim that for the population of statistics final exams, the mean score is 75 using alternative hypothesis that the mean score is different from 75. Sample statistics include n=23, x¯=79 , and s=17. Use a significance level of α=0.05. (Assume normally distributed population.) A) The test statistic is B) The P-value is C) The conclusion is

A) 1.13 B) 0.27 C) There is not sufficient evidence to reject the claim that the mean score is equal to 75

For adult males in the U.S., the distribution of heights (measured in centimeters) is approximately normal with mean 178 and standard deviation of 7.7. A)What is the z-score of a man who is 189 centimeters tall? B)What percentage of this population have heights larger than 189 centimeters? C) What percentage of this population have heights between 178 and 189 cm? D) For a person to be in the top 10% of the population, how tall would they need to be? E) What is the height of a person whose z-score is -2.1?

A) 1.43 B) 8% C) 42% D) at least 188 cm E) 161.5 cm

Researchers are interested in the effect of isolation on the human brain. They used an MRI to measure the volume for the portion of the brain that makes new memories, and applied their techniques to two groups: 15 people who spent 12 months alone in the arctic, and 21 people who formed a control group. For the group that spent time in the arctic they found an average brain-memory-region volume of 332cm3 and a standard deviation of 30cm3. For the control group they found an average volume of 350cm3 and a standard deviation of 40cm3. A) Compute the t-statistic for testing the alternative hypothesis that the mean brain-memory-volume for normal people is larger than that of people who spend time in isolation. The t-statistic for this test: B) What are the degrees of freedom (using the conservative method): C) Find the P-value for the test: D) Is there significant evidence at the 0.05 level to support the hypothesis that people who spend time in isolation have less brain-memory volume?

A) 1.54 B) 14 C) 0.07 D) no

A report in a research journal states that the average weight loss of people on a certain drug is 18 lbs with a margin of error of ±5 lbs with confidence level C = 95%. A) According to this information, the mean weight loss of people on this drug could be as low as what: B) The confidence interval was produced using z-statistics and σ=7 lbs. If the study is repeated, how large should the sample size be so that the margin of error would be less than 2.5 lbs? C) What does 95% confidence mean here?

A) 13 lbs B) at least 31 people C) the methods we used to get the interval yield correct answers 95% of the time

A company sells sunscreen in 450 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean 450 ml and standard deviation 4 ml. A store sells the lotion at a discount if you buy it in packages of four tubes. Consider the amount of lotion from a SRS of 4 tubes of sunscreen. A) The standard deviation of the average x¯ is equal to: B) The probability that the total amount of sunscreen from 4 tubes will be less than 1790 ml is:

A) 2.0 B) 0.11

Justin is interested in buying a digital phone. He visited 10 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 270.12 and a standard deviation of 28.98. A) What t-score should be used for a 95% confidence interval for the mean μ of the price of the phone at all stores?t* = B) Calculate a 95% confidence interval for the mean price of this model of digital phone.

A) 2.262 B) 249.39, 290.85

The UO administration wants to learn more about how important UO students think football is to their college experience. They send out a survey to 2000 students and get 327 responses back. A) The population in this study is B) The sample in this study is

A) All UO students B) The 327 students who responded to the survery

For each prompt select the best response. A) In formulating hypotheses for a statistical test of significance, the null hypothesis is often B) In testing hypotheses, which of the following would be strong evidence against the null hypothesis? C) The P -value of a test of a null hypothesis is which of the following:

A) a statement of "no effect" or "no difference" B) obtaining data with a small P-value C) the probability assuming the alternative hypothesis is true, of getting a test statistic at least as extreme as that actually observed

A study aims to see whether low-sodium diets can improve high blood pressure. 120 women are recruited as subjects, and they are sorted into three age groups of thirty each: 18-30, 31-50, and 51-80. In each age group, the women are randomly assigned either a low-sodium diet or a high-sodium diet, and after four weeks on this diet their blood pressure is monitored. A) What kind of experimental design is this? B) The response variable is C) The age group of the women is what kind of variable? D)What kind of study is this? E) Is there a control group?

A) block design B) blood pressure C) categorical D) experimental E) no

We are testing a drug manufacturer's claim that their drug lowers blood pressure. We choose 100 people and randomly give 50 of them the drug for two weeks, whereas the other 50 get a placebo. The participants do not know who gets which drug, but the kind of drug is marked on their data sheets that are seen by the doctors and nurses who work with them. We measure their blood pressures before the two weeks and after the two weeks. Answer the following questions about this situation: A) This kind of study is: B) Is there a control group? C)Is this a blind study? D)Is this a double-blind study? E)The response variable in this situation is: F)The explanatory variable in this situation is:

A) experimental B) yes C) yes D) no E) blood pressure F) whether or not they took the manufacturers drug

Suppose you are constructing a confidence interval for the mean of a certain variable. A) If you decrease the sample size then the width of the confidence interval will B) If you decrease the confidence level then the width of the confidence interval will

A) increase B ) decrease

We want to calculate an 84%-confidence interval using z-statistics. How do we find the critical value z∗? A) On a calculator: B) In Excel:

A) invnorm(0.92) B) normSinv(0.92)

We want to compute the proportion of observations in a normal distribution having z-value less than -0.3. A)What formula would you use to do this in Excel or Google Sheets? B) What formula would you use to do this on a statistical calculator?

A) normSdist(-0.3) B) normalcdf(-999,-0.3)

On a certain exam, scores are normally distributed with mean 68 and standard deviation 5.3. What proportion of students scored below 60? A) Select which of the following calculator functions will compute the answer: B) Select which of the following Excel functions will compute the answer:

A) normalcdf(-999,-1.51) B) norm.S.dist(-1.51)

Suppose you were testing against Ha:μ<13. You take a SRS of size 48 and get a t-statistic equal to −2.3. A) What Excel/Google-Sheets command would we use to find the P-value (we have listed equivalent options, with the Excel command first)? B) What calculator command would we use to find the P-value?

A) t.dist(-2.3,47,1) B) tcdf(-999,-2.3)

In the following situations, determine which of the following statistical procedures is appropriate. A) You wish to determine whether the average lifespan of blue herons (a kind of bird) in Oregon is different from the average lifespan of blue herons in Florida. You select a random sample of 100 records from the Oregon Audobon Society, and another random sample from the Florida Audobon Society. Then you compute the average lifespans for the two samples and compare them. B) You wish to test whether the average age of undergraduates at UO is more than 20. You choose at random 100 current UO undergraduates and calculate their average age. C) You wish to test whether seeing a picture of a salty food can make a person feel thirsty. You design a "thirst survey" and give it to 50 subjects, measuring their average score. Then you show the subjects pictures of salty foods and given them the same survey afterwards, again computing the average score.

A) two-sample t-test B) one-sample t-test C) matched pairs t-test

In each case choose the phrase or term that best applies to the given situation: A) After making a purchase at Walmart you are given a receipt with a survey you can fill out about your experience with the store. B)We want to survey what Oregonians think about global warming. For each county we randomly select 100 people for this study. C)We want to survey what students in our Math 243 class think about online learning. We assign a unique number to each student and have a computer randomly select 50 students for us to talk to.

A) voluntary response sample B) stratified random sample C) simple random sample

If scores on an exam are normally distributed with mean m and standard deviation 25, how high would a person have to score in order to be in the top 2.5 percent? Use the 68-95-99.7 rule to determine the correct value.

At least m+50

One year the scores on the ACT test followed the N(26,2.7) distribution, whereas scores on the SAT followed N(944,159). Mai got a 1020 on the SAT and her friend Pat got a 28 on the ACT. How would you determine who did better, in terms of who scored in a higher percentile?

Compute the z-scores and take the larger one

You conduct a poll by standing outside the EMU and asking students walking out of the building whether they think puppies, kittens, or piglets are the cutest of the three. What sort of sample is this?

Convenience sample

Consider the data sets D1={2,2,3,5,5,7,8,8}, D2={3,3,4,4,4,5,5,5}, and D3={1,1,1,2,6,9,9,10}. The data set with the largest standard deviation is

D3

Psychologists have produced a new test of intelligence. Extensive testing on humans has shown that the average score is 52.3. John takes the test and scores a 75. Which of the following represents the best conclusion?

John has above average intelligence, but we can't really judge how far above average because we don't know the standard deviation.

Heights of women follow the N(66,2.5) distribution, whereas heights of men follow the N(69,2.1) distribution. What proportion of women are shorter than the mean height for men? Select the calculator function that would compute this:

Normalcdf(-999,69,66,2.5)

Without using your calculator or any technology, find the quartiles for the following data: 23, 52, 63, 67, 37, 69, 71, 63, 43, 69, 61, 25

Q3=68 Q2=62 Q1=40

Scores on a certain exam follow the normal distribution N(68,12). How high do you have to score in order to be in the top 10 percent? Identify the steps for solving this problem: Step 1: Step 2:

Step 1: z=invnorm(0.90) Step 2: Compute 68+12*z

Which of the following statements is true about the t-distributions?

The greater the degrees of freedom, the more the t-distribution resembles the standard Normal distribution.

What is the reason we sometimes use a t-test instead of a z-test?

The z-test isn't applicable if we don't know the population standard deviation, but the t-test is.