A simple random sample of 1500 voters were surveyed and asked whether they were planning to vote for the incumbent mayor for re-election. Seven hundred ninety-eight of them replied that they were planning to vote for the mayor. The mayor claims that more than half of all voters are planning to vote for her. To test this claim, a test of the hypotheses H0: p = 0.5 versus H1: p > 0.5 is performed. a. Show that the P-value is 0.007. b. The P-value is very small, so H0 is rejected. A pollster claims that because the P-value is very small, we can be fairly certain that the population proportion p is greater than 0.5, but we cannot be certain that it is a lot greater. Is this a correct interpretation of the P-value?

Question

Who will you vote for? A simple random sample of 1500 voters were surveyed and asked whether they were planning to vote for the incumbent mayor for re-election. Seven hundred ninety-eight of them replied that they were planning to vote for the mayor. The mayor claims that more than half of all voters are planning to vote for her. To test this claim, a test of the hypotheses H0: p = 0.5 versus H1: p > 0.5 is performed.

a.

Show that the P-value is 0.007.

b.

The P-value is very small, so H0 is rejected. A pollster claims that because the P-value is very small, we can be fairly certain that the population proportion p is greater than 0.5, but we cannot be certain that it is a lot greater. Is this a correct interpretation of the P-value?

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

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: The following data represents the GPA of a sample of 15 students enrolled in a math class. Use techn...

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to ou...

Q: A business consultant wanted to investigate whether providing daycare facilities on the company prem...

A: Hey, since there are multiple subparts posted, we will answer first three question. If you want any ...

Q: ind the indicated z score. The graph depicts the standard normal distribution with mean 0 and standa...

A: Given: The z value corresponding to area 0.9406 is calculated by Excel command NORM.S.INV(0.9406).

Q: In a recent survey at a small Midwestern college, 39 of 140 randomly selected students revealed that...

A: Here it is given that- total number of observations(n) = 140 Proportion (p) = 39140= 0.28 So, q = 1-...

Q: CONFIDENCE INTERVALS FOR THE DIFFERENCE IN 2 POPULATION MEANS Children in two elementary school clas...

A: We have been given that the confidence interval is (-10, -2) The confidence interval does not includ...

Q: Express the confidence interval (0.050,0.112)in the form of p−E<p<p+E.

A: From the given information, the confidence interval is (0.050, 0.112) p = (Upper bound + lower bound...

Q: A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptom...

A: This is two proportions Z-test. Rejection criteria: Reject the null hypothesis if |Z|>Zc at 0.05 ...

Q: Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text....

A: Given Information: p = 26.1% = 0.261 Sample size (n) = 317 x = 61 are of the type two short and thre...

Q: The mean age that cats get adopted at a shelter is 21.4 months with a standard deviation of 3.6 mont...

A: Solution: Let X be the age. From the given information, X follows normal distribution with mean µ=21...

Q: Assume a population of 1​, 3​, and 8. Assume that samples of size n=2 are randomly selected with rep...

A: Given Values, Population: 1, 3, 8 N = 3 Calculate the population mean Calculate the population stan...

Q: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit...

A: Let "X" be the distance of fly balls hit to the outfield (in baseball). Draw the normal curve an...

Q: Need help with explanation and answer

A: Consider two points (x1, y1) and (x2, y2). Then, the regression equation is, (y – y1)/(x – x1) = (y2...

Q: A normal distribution has a mean of u=54 and a standard deviation of o=6, what is the probability of...

A:  

Q: Find the area of the shaded region. The graph depicts the standard normal distribution of bone densi...

A: Click to see the answer

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the ind...

A: Given, X follows normal distribution with mean 8 and standard deviation 2. X~N(μ=8,σ2=22)

Q: Please see problem with the solution: after reviewing the information below, assess the appropriaten...

A: The important results that can be seen in the analysis are, 1)R-Sq 2)estimate of  error standard dev...

Q: Express the confidence interval 0.111<p<0.333 in the form p±E.   p±E=_____±____

A: According to the provided information, the confidence interval 0.111<p<0.333 in the form p±E.

Q: The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers. Comp...

A: Joint pdf of X & Y is        f(x,y)=1/6;  0≤x+y≤2, x,y>00  ; elsewhere Marginal pdf of X is  ...

Q: Depths of pits on a corroded steel surface are normally distributed with mean 822 µm and standard de...

A: Click to see the answer

Q: A distribution of sample means with scores of 35 were taken from a skewed population. The distributi...

A: According to central limit theorem, for large sample (>30) or if the population follows normal di...

Q: A sample of n = 5 scores has ΣX = 20 and ΣX2 = 180. For this sample, what is the value of the sample...

A: According to the provided information,   n = 5  ΣX = 20 ΣX2 = 180  

Q: A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 2...

A: Given, Mean μ = 55 standard deviation σ = 14 random sample size n = 25    

Q: QUESTION 42 What is the appropriate statistical test to assess whether there is an association ...

A: Chi-square test of independence:   A single simple random sampling is done with each individual bein...

Q: NORMAL DISTRIBUTION A radar unit is used to measure speeds of cars on a highway. The speeds are norm...

A: Let X denote the driving speed. Therefore, X~N (µ=75, σ=10.5) Given, that the driver will get a tick...

Q: An investigation is carried out to determine whether face to face or virtual learning is more effect...

A: (1). Construct a pdf for both sets of data: Given data represents the scores of 12 students who took...

Q: What is the sensitivity and specificity for each of the screening tool values? New Screening Too...

A: Sensitivity: The formula for sensitivity is obtained as given below: Sensitivity=Number of true posi...

Q: the manager of a computer retails store is concerned that his suppliers have been giving him laptop ...

A: A. Let x¯ denotes the mean replacement time which follows normal distribution. The mean is 3.4 years...

Q: A car manufacturer asserts that with the new collapsible bumper system, the mean body repair cost fo...

A: Given data: The mean body repair cost for the damage sustained in a collision impact of 15 miles per...

Q: Find the value of the test statistic. W = What is the p-value? (Round your answer to four decimal pl...

A: The null and alternative hypotheses are as follows; Ho: The two populations of flight delays are ide...

Q: Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores a...

A: Let Q denote the random variable that represents the IQ scores of adults and q be a realization of Q...

Q: Could you please solve exercise 3_2 a,b,c

A: (a). Identify the dataset with larger variation: The mean of dataset-I is x1 - bar = 50. The standar...

Q: The probability density function f(x) for a uniform random variable X defined over the interval [2,1...

A: Click to see the answer

Q: a. Holmes Institute conducted a survey about International Students in Melbourne. Thesurvey results ...

A: The row and column total is given below:   Yes No   23 and under 207 201 408 24-26 299 379 6...

Q: Question 1 An analyst is interested in testing the hypothesis Ho : µ <15,000. The data consist ...

A: Given Information: An analyst is interested in testing the hypothesis Ho : µ <15,000.  Sample siz...

Q: For a population with a mean of  μ = 50 and a standard  deviation of  σ = 10, compute the standard e...

A: Mean = 50 Standard deviation = 10

Q: Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all...

A: Let "X be the hip breadths for men. Find z-value (z): Refer Standard normal table/Z-table, Lookup...

Q: A sample of n = 4 scores has a mean of M = 75. Find the z-score for this sample: a. If it was obtain...

A: Sample Mean = 75 Sample size = 4

Q: Assume that adults have IQ scores that are normally distributed with a mean of 100.5 and a standard ...

A: Mean = 100.5 Standard deviation = 17.5

Q: A simple random sample of 37 men from a normally distributed population results in a standard deviat...

A: The hypotheses are given below:Null hypothesis: H0:σ=10 Alternative hypothesis: Ha:σ≠10 The test sta...

Q: An internet service provider​ (ISP) has experienced rapid growth in the past five years. As part of ...

A: Sample mean = (288+333+281+308+311+343+305+289+284+386+358+330)/12 = 3816/12 = 318

Q: The population weights of a particular fruit is normally distributed, with a mean of 689 grams and a...

A: Given: μ = 689 σ = 30 n = 18 The value of z at 4%, i.e., corresponding to the right to the 4% area o...

Q: Employer-based health insuranceA report from a Gallup poll1 in 2011 started by saying, "Forty-five p...

A: From the provided information, Forty-five percent of American adults reported getting their health i...

Q: True or False?:a. The distribution of sample means will always be normal if taken from a normal popu...

A: a) We know that, if the population is normally distributed then the distribution of sample means wil...

Q: A multinational corporation employing several thousand workers at its campus in a large city would l...

A: A multinational corporation employing several thousand workers at its campus in a large city would l...

Q: Suppose the random variable xx has a normal distribution with μ=300μ=300 and σ=30σ=30. Find the valu...

A: Given: μ=300, σ=30.

Q: The weights of radish seeds are normally distributed, with µ = 0.12 g and σ = 0.02 g.     What is th...

A: Z score is the score used to measure by how many units the value of a raw score is above or below th...

Q: Please answer D :)

A: Here, n = 39 and p = 0.82

Q: Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a n...

A: d) It is given that the birth weights are normally distributed with mean μ=3,500 grams and standard ...

Q: Salaries of 48college graduates who took a statistics course in college have a​ mean,x​, of $66,400....

A: Click to see the answer