Canvas Final Exam Review Notes 3

Please find the confidence interval formula, if sample mean is 15 and s = 1.2; Assume it is normally distributed. Which equation should be used to construct the 95% confidence interval for the population mean?

(x̄ - t(α/2) * s/√n , x̄ + t(α/2) * s/√n)

Please find the confidence interval formula, if the sample size is 75 and s = 1.2; Which equation should be used to construct the 95% confidence interval for the population mean?

(x̄ - z(α/2) * s/√n , x̄ + z(α/2) * s/√n)

The following two-way contingency table relating the result of a test for a disease and the health with respect to that disease of the person tested Diseased/Healthy/Total Positive: 0.043, 0.007, 0.05 Negative: 0.016, 0.914, 0.93 Inconclusive: 0.001, 0.019, 0.02 The probability that a randomly selected person is either Tested positive or has disease?

0.067 0.05 + 0.06 = 0.11 0.11 - 0.043 = 0.067

The following table gives the probabilities of all parts made from two production lines at a factory whether they are good or defective. A part is randomly selected from this factory. The probability that this part is defective is about Line 1/Line 2 Good: 0.40, 0.50 Defective: 0.025, 0.075

0.10 0.025 + 0.075 = 0.10

The probability distribution of a discrete random variable X is shown in the following table: X: -3, 2, 3, 4, 5 p(x): 0.14, 0.26, 0.15, 0.35, 0.1 Find P(x < -0.5) Find P(x > -0.5)

0.14 0.86

The probability distribution of a discrete random variable X is given by X: 0, 1, 2, 3, 4 p(x): ?, 0.28, 0.17, 0.15, 0.01 Find the missing probability in the table.

0.39 0.28 + 0.17 + 0.15 + 0.01 = 0.61 1 - 0.61 = 0.39

The following two-way contingency table gives the breakdown of the voters in a particular locale according to gender and political party preference. A person is selected at random from this population. Democratic/Republic Male: 0.24, 0.28 Female: 0.29, 0.19 Let A be the event that the selected person will vote for Republic party; B be the event that the selected person is a female. Find P(A U B)?

0.76 0.28 + 0.19 + 0.29 = 0.76

The following two-way contingency table relating the result of a test for a disease and the health with respect to that disease of the person tested Diseased/Healthy Positive: 0.043, 0.007 Negative: 0.016, 0.914 Inconclusive: 0.001, 0.019 The probability that a randomly selected person is healthy (free of the disease) is about

0.94 0.007 + 0.914 + 0.019 = 0.94

Cell phone bills in a city's residents have a mean of $64 and a standard deviation of $14. Random samples of 100 bills are drawn from this population, and the mean of each sample is found. What is the sampling error of the mean?

1.4

A company conducts a survey of 500 randomly selected individuals to get their overall impressions of the past year. Results are shown below. What is the probability that the next person surveyed has a "Do not like (negative)" impression? Response/Frequency Like: 280 Do not like: 200 Don't Know: 20 Total: 500

200/500 = 0.40

Cell phone bills in a city's residents have a mean of $64 and a standard deviation of $14. Random samples of 100 bills are drawn from this population, and the mean of each sample is found. What is the mean of the sampling distribution?

64

Which of the following formula will be used to find the mean of the discrete distribution?

= ∑ x*p(x)

A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 54 g. He randomly samples 73 sodas. Assume the population is normally distributed and suppose the test statistic is -1.19. Which function in Excel finds the p-value?

=1-NORM.DIST(-1.19, 0, 1, TRUE)

How would you find the mean of data in the range B2 to B42 in Excel?

=AVERAGE(B2:B42)

Which of the following Excel functions will find the critical value of zα/2 with the confidence level of 98%?

=NORM.INV(0.02/2, 0, 1)

Using Excel, how would you find the standard deviation for a sample of data located in cells A2 to A6?

=STDEV.S(A2:A6)

A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 54 g. He randomly samples 13 sodas. Assume the population is normally distributed and suppose the test statistic is -1.19. Which function in Excel finds the p-value?

=T.DIST(-1.19, 12, TRUE)

Given a T distribution with the degrees of freedom of 24. (n = 25) Which function finds the probability that T is less than 1.2 Which function finds the probability that T is more than 1.2

=T.DIST(1.2, 24, true) =1-T.DIST(1.2, 24, true)

A survey shows that people use cell phones an average of 1.3 years with a standard deviation of 0.4 years. A user is randomly selected. If cell phone use is normally distributed, we can use Excel to calculate the probability that the randomly selected user uses their phone for less than 1 year with the function: more than 1 year with the function:

=norm.dist(1,1.3,0.4,true) =1-norm.dist(1,1.3,0.4,true)

The score made by a particular student on SAT test is the 87th percentile. This means that

About 87% of all scores on the test were equal to or less than his

There are three explanations and definition 1. Alpha is Probability of Type 1 error occuring, called level of significance the maximum allowable probability of rejecting the null hypothesis when its true 2. Betta is Probability of Type 2 error occuring 3. The p-value is known as the probability value. It is defined as the probability of getting a result that is either the same or more extreme than the actual observations. The p-value is known as the level of marginal significance within the hypothesis testing that represents the probability of occurrence of the given event. The p-value is used as an alterative to the rejection point ot provide the least significance at which the null hypothesis would be rejected. If the p-value is small, then there is stronger evidence in favour of the alternative hypothesis. P-value <= Alpha: Reject H0. P-value is always between 0 and 1.

All true (1, 2, 3)

The mean score on a standardized math exam 79.2; the standard deviation is 8.3. Bill is told that the z-score of his exam score is -1.2. Is Bill's score above average or below average? Adam's z-score is 1.35, is Adam's above average or below average?

Bill = below average Adam = above average

There were 100 students who took part in the common final exam on STAT 1222. THe average is 77 with a standard deviation of 7. If a student got a z-score of 2.95 in this exam, which of the following is true?

Compared with the other students in this exam, this student did extremely well.

When a Type 1 error occurs

H0 is wrongly rejected when it is actually true

A standard painkiller is known to bring relief in 3.5 minutes on average (μ). A new painkiller is hypothesized to bring faster relief to patients. A sample of 40 patients are given the new painkillers. The sample yields a mean of 2.8 minutes and a standard deviation of 1.1 minutes. Which of the following pairs of hypotheses are appropriate for this study?

H0: μ ≥ 3.5 Ha: μ < 3.5 (claim)

Seven bear tracks were found in the woods. Their length was measured in inches and recorded in the table below: 9.25, 9.25, 9.4, 9.5, 9.6, 9.6, 9.6 If another bear track was found that was 7.8 in, what would happen to the mean?

It would decrease

An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and uses α = 0.05 to test the claim. Suppose the p-value is 0.003 What is the decision?

Reject H0 since the p-value is less than the significance level.

Let Z be the random variable which has the standard normal distribution N(0,1). Which of the following is NOT a property of the standard normal distribution?

The potential values of Z are from -3 to 3

A survey was conducted to estimate the proportion of all eligible voters who actually voted in the previous presidential election. The survey investigated 1800 eligible voters and found that 1560 86.6% of them actually voted. Which of the following is true?

The sample size is 1800

You are buying a lottery ticket. Let X = 1 if you win the lottery and X = 0 if you lose. Which of the following tables represents the resulting probability distribution for the random variable X? P(Win) = 0.01

X: 0, 1 p(x): 0.99, 0.01

In a random sample of 900 woman, 198 say they are in favor of "A" brand. Let p be the proportion of all woman who are in favor of "A" brand. A researcher wishes to test the following hypotheses: H0: p = 0.20; Ha: p > 0.20 In this scenario p̂ = [blank 1] and p0 = [blank 2] Test statistic z = p̂ - p0/√(p0*q0)/n

[blank 1] = 0.22 [blank 2] = 0.20

A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 12 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use α = 0.01 to test the claim. In this scenario, the appropriate test statistic is: a) z = (p̂ - p0)/√(p0*q0)/n b) z = (x̄ - μ0)/(s/√n) c) t = (x̄ - μ0)/(s/√n)

c

17% of victims of financial fraud know the perpetrator of the fraud personally. Let X be the number of people in a random sample of 36 victims of financial fraud who knew the perpetrator personally. Then X is binomial with: n = p = mean = variance =

n = 36 p = 0.17 mean = n*p variance = n*p*(1-p)

Range, variance and standard deviation measure the ____ of a data set while mean, median, and mode are all measures of the ___ of a data set

spread; central tendency

The level of significance is _____

the maximum allowable probability of rejecting the null hypothesis when its true

A researcher wishes to estimate the average amount spent per person by visitors to a museum. She takes a random sample of fifty-five visitors and obtains an average of $27.5 per person. The population of interest is...

visitors to the museum

If every else remain the same which of the following confidence level will result the widest confidence interval? Which one is the narrowest confidence interval?

widest: 99 narrowest: 80

In a random sample of 500 students, 136 say they are in favor of traveling NC. Let p be the proportion of all students who are in favor of traveling in NC. One is interested for the following hypotheses: H0: p ≥ 0.35 vs. Ha: p < 0.35 (claim) Which of the following represents the standardized test statistic?

z = p̂ - p0/√(p0*q0)/n