The standard deviation of SAT scores for students at a particular Ivy League college is 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 25 points. (a) Raina wants to use a 90% confidence interval. How large a sample should she collect? (b) Luke wants to use a 99% confidence interval. Without calculating the actual sample size, determine whether his sample should be larger or smaller than Raina’s, and explain your reasoning. (c) Calculate the minimum required sample size for Luke.

Question

The standard deviation of SAT scores for students at a particular Ivy League college is 250
points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this
college as part of a class project. They want their margin of error to be no more than 25 points.
(a) Raina wants to use a 90% confidence interval. How large a sample should she collect?
(b) Luke wants to use a 99% confidence interval. Without calculating the actual sample size, determine
whether his sample should be larger or smaller than Raina’s, and explain your reasoning.
(c) Calculate the minimum required sample size for Luke.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Other

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Consider the hypotheses below.  H0 u = 50. H0 u≠ 50  Given that x= 53, s= 20, n= 25, and a= 0.05, an...

A: a) degrees of freedom=n-1=25-1=24 α=0.05 Given test is two tail test. t critical=±2.064, from the ex...

Q: Answer part B

A: b). Given, NOX/NMOG emissions over the useful life for one car model vary normally with mean 78mg/mi...

Q: ?

A: Policy: Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: You want to obtain a sample to estimate a population proportion. At this point in time, you have no ...

A: Click to see the answer

Q: The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-sh...

A: Let "X" be the number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania. ...

Q: The standard deviation of SAT scores for students at a particular Ivy League college is 250points. T...

A: Given, σ = 250Margin of Error = 25         To find, a) Find sample ize for raina's 90% confidene int...

Q: 1. You hear a lot of discussion about COVID tests these days. For some of these tests, the so-called...

A: Introduction: The results of any test, especially a test to determine the presence or absence of a d...

Q: With a sample size of 12, the P(t<x)=0.56 What is x?   The cost of textbooks is normally distribu...

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you re...

Q: In a mid-size company, the distribution of the number of phone calls answered each day by each of th...

A: Let "X" be the number of phone calls answered each day.  

Q: A person wants to determine which of two routes to drive has the shorter average driving time. Time ...

A: a) Null Hypothesis: H0: The mean score for A is not less than the mean score for B. Alternative Hypo...

Q: Home Internet Access In a recent year, a study found that 75% of adults ages 18–29 had internet acce...

A: Solution: Let X be the number of undergraduates had internet access and n be the sample number of un...

Q: Find the probability that Maggie will see at least 3 clients per day (round four decimal place). Fin...

A: Given frequency table: Total frequency is 225 Probability(x) = frequency(x) / total frequency Proba...

Q: According to a Yale program on climate change communication survey, 71% of Americans think global wa...

A: (a) The binomial probability distribution is, PX=x=nxpx1-pn-x In the formula, n denotes the number o...

Q: Use the given data to find the minimum sample size required to estimate the population proportion.  ...

A: Find z-critical value: https://drive.google.com/file/d/1S_b_En4yZMZPhsaGfBA2eE_M0IJFOVeW/view?...

Q: Statistics Question

A: Sketch the normal curve and shade the area of 0.04 to the left of "z" under the normal curve. Refer...

Q: The genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase t...

A: a.   Obtain the best point estimate of the population proportion of boys born to parents using the Y...

Q: Many Americans believe that women talk more than men. A 1998 study tested this theory by evaluating ...

A: The two sample t-test statistic is, t=x¯M-x¯WsM2nM+sW2nW=12,867-16,4968,343220+7,914227=-3,6292,408....

Q: In a survey, 26 people were asked how much they spent on their child's last birthday gift. The resul...

A: As the population standard deviation is not known, we will use t-distribution. Xˉ=35.8 s=4.9 n=26  T...

Q: 5. A marketing research firm surveyed 49 randomly selected residents in North Texas to determine the...

A: Click to see the answer

Q: Assume a significance level of a = 0.05 and use the given information to complete parts (a) and (b) ...

A: Click to see the answer

Q: Students at a school took a 35-point exam.  Below is a random sample of exam scores. 25        35   ...

A: Given data of sample scores25  35  22  19  25  31  21  27  10  22 a)Class width =6The range of data ...

Q: You want to obtain a sample to estimate a population proportion. At this point in time, you have no ...

A: Obtain the sample size of a no preliminary estimate for p. The formula of sample size is, Use EXCEL...

Q: Find the indicated​ z-scores shown in the graph.

A: From the given diagram, P(z1<Z<z2)=0.4783+0.4783=0.9566P(Z<z1)=0.0217P(Z>z2)=0.0217

Q: In a clinical trial, 18 out of 820 patients taking a prescription drug daily complained of flulike s...

A: Given information- Population proportion, p = 0.017 Sample size, n = 820 Significance level, α = 0.0...

Q: For a one-sample ? test with ?? = 40, find the P-values of the following hypothesis tests.  (a) ?0 :...

A: The p-value can be obtained by using the t-distribution table. (a) The test is two-tailed as the alt...

Q: The following data has been collected on the number of times that owner-occupied and renter-occupied...

A: Solution: Let x = number of times that owner-occupied units had a water supply stoppage lasting 6 or...

Q: Needed Answer: d. only

A: Click to see the answer

Q: Diotrbuto of f students colleye ages 215 6=3 Sample n= 36 probabi lity f what is 8 average age betwe...

A: Since the sample size is greater than 30, According to the central limit theorem (CLT), the distribu...

Q: -2 Fit data to the exponential model by using linearization. Find the 2-norm of the difference 4 bet...

A: Given: The exponential model follows the linearization in which the data point’s yi and the value of...

Q: Exhibit 3 You are given the following information about y and x. Dependent Variable y Independent Va...

A: Introduction: Consider that x is the independent variable and y is the dependent variable. The size ...

Q: Assume that a sample is used to estimate a population mean μμ. Find the 95% confidence interval for ...

A: Obtain the 95% confidence interval for the population mean. The 95% confidence interval for the popu...

Q: state whether the parameter of interest is a mean or a proportion: a poll shows that 64% of American...

A: Mean statsitic comes under study if we are studying averages of the numerical data, for example, age...

Q: Determine the test statistic and identify the p value, thank you.

A: Click to see the answer

Q: Assume a member is selected at random from the population represented by the graph. Find the probabi...

A: Here μ = 20.9 and  σ = 5.2 We Know that, Z = X-μσ then, When X= 27,                     Z= 27-20.95....

Q: STATE: Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks...

A: The mean annual return for common stocks for 40 years will follow normal distribution with parameter...

Q: The number of seconds XX after the minute that class ends is uniformly distributed between 0 and 60....

A:  X after the minute that class ends is uniformly distributed between 0 and 60. 1. The distribution o...

Q: Find the z-score, to the nearest hundredth, that satisfies the given condition. 0.198 square unit of...

A: P(Z<z)=0.198 square unit z=?

Q: Find the area, to the nearest thousandth, of the indicated region of the standard normal distributio...

A: P(z < −0.75 )=?  

Q: In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with gar...

A: Obtain the 95% confidence interval estimate of the mean net change in LDL cholesterols after the gar...

Q: Do Predicted Temperatures match Actual Temperatures? The table shows the predicted and actual temper...

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case yo...

Q: The figure to the right shows the results of a survey in which 1013 adults from Country A, 1001 adul...

A: Click to see the answer

Q: Do single-parent families tend to be more impoverished than familics with two parents? In to test if...

A: Given table data is as below,   col1 col2 totals row1 24 20 44 row2 11 45 56 totals 35 65 N...

Q: From a box containing four 5-Peso coins and three 10-Peso coins, three coins are selected at randomw...

A: Click to see the answer

Q: In a certain instant lottery game, the chance of a win is stated as 13%. Express the indicated degre...

A: According to the provided information, In a certain instant lottery game, the chance of a win is sta...

Q: You want to obtain a sample to estimate a population proportion. At this point in time, you have no ...

A: From the provided information, Margin of error (E) = 0.03 Confidence level = 98% Assuming the popula...

Q: Samuel Morse determined that the percentage of a's in the English language in the 1800s was 8%. A ra...

A: Denote p as the true proportion of a’s in modern newspaper. It is reported that proportion of a’s in...

Q: About 10% of Olympic athletes use illegal performance drugs.  A test for the presence of these drugs...

A: Here it is given that about 10% of Olympic athletes use illegal performance drugs and a test for the...

Q: The human resources manager of a consumer product company asked a random sample of employees how the...

A: Given, α = 0.10 Work Status Very Interesting Fairly Interesting Not Interesting Total ...