In a certain school district, it was observed that 27% of the students in the element schools were classified as only children (no siblings).  However, in the special program for talented and gifted children, 117 out of 342 students are only children.  The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.01α=0.01 level of significance. What is the hypothesized population proportion for this test? p=p= (Report answer as a decimal accurate to 2 decimal places.  Do not report using the percent symbol.) Based on the statement of this problem, how many tails would this hypothesis test have? one-tailed test two-tailed test Choose the correct pair of hypotheses for this situation:   (A) (B) (C) H0:p=0.27H0:p=0.27 Ha:p<0.27Ha:p<0.27 H0:p=0.27H0:p=0.27 Ha:p≠0.27Ha:p≠0.27 H0:p=0.27H0:p=0.27 Ha:p>0.27Ha:p>0.27   (D) (E) (F) H0:p=0.342H0:p=0.342 Ha:p<0.342Ha:p<0.342 H0:p=0.342H0:p=0.342 Ha:p≠0.342Ha:p≠0.342 H0:p=0.342H0:p=0.342 Ha:p>0.342Ha:p>0.342   (A) (B) (C) (D) (E) (F) Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion?  z=z=   (Report answer as a decimal accurate to 3 decimal places.) You are now ready to calculate the P-value for this sample.  P-value =   (Report answer as a decimal accurate to 4 decimal places.) This P-value (and test statistic) leads to a decision to...  reject the null accept the null fail to reject the null reject the alternative As such, the final conclusion is that...  There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. The sample data support the assertion that there is a different proportion of only children in the G&T program. There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T progra

Question

In a certain school district, it was observed that 27% of the students in the element schools were classified as only children (no siblings).  However, in the special program for talented and gifted children, 117 out of 342 students are only children.  The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.01α=0.01 level of significance.

What is the hypothesized population proportion for this test?
p=p=
(Report answer as a decimal accurate to 2 decimal places.  Do not report using the percent symbol.)

Based on the statement of this problem, how many tails would this hypothesis test have?

  • one-tailed test
  • two-tailed test



Choose the correct pair of hypotheses for this situation:

 

(A) (B) (C) H0:p=0.27H0:p=0.27
Ha:p<0.27Ha:p<0.27
H0:p=0.27H0:p=0.27
Ha:p≠0.27Ha:p≠0.27
H0:p=0.27H0:p=0.27
Ha:p>0.27Ha:p>0.27
  (D) (E) (F) H0:p=0.342H0:p=0.342
Ha:p<0.342Ha:p<0.342
H0:p=0.342H0:p=0.342
Ha:p≠0.342Ha:p≠0.342
H0:p=0.342H0:p=0.342
Ha:p>0.342Ha:p>0.342

 

(A)
(B)
(C)
(D)
(E)
(F)



Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion? 
z=z=  
(Report answer as a decimal accurate to 3 decimal places.)

You are now ready to calculate the P-value for this sample. 
P-value =  
(Report answer as a decimal accurate to 4 decimal places.)

This P-value (and test statistic) leads to a decision to... 

  • reject the null
  • accept the null
  • fail to reject the null
  • reject the alternative



As such, the final conclusion is that... 

  • There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program.
  • There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program.
  • The sample data support the assertion that there is a different proportion of only children in the G&T program.
  • There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T program.

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 segmented bar graphs below depict data from the NAAL (National Assessment of Adult Literacy) con...

A: Solution: There exists relationship among volunteerism-never, Less than once per week and Once per w...

Q: Pets The American Veterinary Association claims that theannual cost of medical care for dogs average...

A: Note: Hey, since multiple sub parts are posted, we will answer first three sub parts according to ou...

Q: The mean and standard deviation of a normal variable X are given. Find the indicated probability. (R...

A: From the given information, the random variable X has mean µ=0 and σ=4.

Q: A researcher is interested in finding a 90% confidence interval for the mean number minutes students...

A: Click to see the answer

Q: We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adul...

A: Click to see the answer

Q: Elephants and hippos We removed humans from thescatterplot in Exercise 31 because our species was an...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

Q: A company has a policy of retiring company cars; this policy looks at number of miles driven, purpos...

A: The provided information are: Population mean (µ) = 61 Population standard deviation (σ) = 10  

Q: Combining scores again The first Stat exam had a meanof 80 and a standard deviation of 4 points; the...

A: The provided information are: For first exam: Population mean (µ) = 80 Standard deviation (σ) = 4 Fo...

Q: Matching Here are several scatterplots. The calculatedcorrelations are -0.923, -0.487, 0.006, and 0....

A: The scatter plots gives the graph of the two variables from which one can depict the relationship be...

Q: Another car The correlation between a car’s horsepower and its fuel economy (in mpg) is r = -0.869. ...

A: Click to see the answer

Q: Dishwashers Dan’s Diner employs three dishwashers. Alwashes 40% of the dishes and breaks only 1% of ...

A: Let A represent person Al, B represent Betty and C represent Chuck. Also, D denotes that dish was br...

Q: H0 :  µ= 60 H1 :  µ &gt; 60  X̄=62    σ=10    n=100 and α=.05 The computed value of  Z (Zc ) or  t (...

A: Click to see the answer

Q: Titanic On the Titanic, the probability of survival was0.323. Among first class passengers, it was 0...

A: Click to see the answer

Q: A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older su...

A: Here, sample size, n is 20, sample mean is 81.8 and sample standard deviation is 23.3.

Q: Save the grapes. Vineyard owners have problems withbirds that like to eat the ripening grapes. Some ...

A: Researchers have information about the save the grapes. The diagram displaying the design of experim...

Q: Statistics Question

A: Click to see the answer

Q: You may need to use the appropriate technology to answer this question. Consider the following hypot...

A: Click to see the answer

Q: You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based...

A: Click to see the answer

Q: In a survery of 259 households, a Food Marketing Institute found that 174 households spend more than...

A: Click to see the answer

Q: You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based...

A: It is given that:

Q: An advertising agency is testing the effectiveness of anew commercial. They are trying out the comme...

A: Solution: The factor of the experiment is the length and format. The factor length is classified int...

Q: Use the confidence level and sample data to find a confidence interval for estimating the population...

A: From the given information, the sample size is 46 and the sample average is 23.1 pounds. The populat...

Q: For this problem, carry at least four digits after the decimal in your calculations. Answers may var...

A: Click to see the answer

Q: Mayoral race Hoping to learn what issues may resonate with voters in the coming election, the campai...

A: a. Identify the population of interest for the given study. To examine the issues that resonate with...

Q: In exercise 7 a sales manager collected the following data on x = annual sales and y = years of expe...

A: It is given that x and y are defined as annual sales and years of experience, respectively. The esti...

Q: A magazine published data on the best small firms in a certain year. These were firms that had been ...

A: Click to see the answer

Q: The hexadecimal digits are as follows: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. How many different sequences...

A: Since, letters A, B, C, D, E, and F are the digits in terms of hexadecimal. Hence, there are 16 digi...

Q: Cramming One Thursday, researchers gave studentsenrolled in a section of basic Spanish a set of 50 n...

A: Click to see the answer

Q: IQs revisited Based on the Normal model N(100, 16)describing IQ scores, what percent of people’s IQs...

A: Given: Population mean (µ) = 100 Standard deviation (σ) = 16 Consider, X be the random variable that...

Q: Listed below are speeds (mi/h) measured from traffic on a busy highway. This simple random sample wa...

A:  

Q: The mean weight of female dancers in a local modern dance company is more than 127 lbs. Express the ...

A: Solution: From the given information, the claim is that the mean weight of female dancers in a local...

Q: Traffic headaches A study of traffic delays in 68 U.S.cities found the following relationship betwee...

A: The data represents the relationship between the total delay of traffic in hours and main highway sp...

Q: Giving a test to a group of students, the grades and gender are summarized below ABCTotalMale1851639...

A: The given summary table is, From the table, the known values are,  Let p represent the percentage ...

Q: West High wants to estimate the number of students who drive to school. Answer the following. ...

A: a). Since, a sample is a part of the population and that represents the population. Therefore, the n...

Q: Họ : p= 60 H1: p> 60 X=62 0=10 n=100 and a=.05 The decision of the test is: ассept Ho not enough evi...

A: Solution: State the hypotheses. Null hypothesis: Alternative hypothesis: Here, the test is right-t...

Q: In a survey, 23 people were asked how much they spent on their child's last birthday gift. The resul...

A: Click to see the answer

Q: A newsgroup is interested in constructing a 90% confidence interval for the difference in the propor...

A: Click to see the answer

Q: Consider the following hypothesis test. H: o, 2 = 0. H: 0, 02 (a) What is your conclusion if n, = 21...

A: Obtain the value of the test statistic. The formula to obtain the value of the statistic is, The for...

Q: A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Liste...

A: Click to see the answer

Q: Testing a Claim about a mean (σ unknown) Suppose the EPA was suing the city of Rochester for non-com...

A: Given, The hypothesis to be tested here is: This is a right tailed test.

Q: The weights of ice cream cartons are normally distributed with a mean weight of 12 ounces and a stan...

A: Given information- Population mean, μ = 12 ounces Population standard deviation, σ = 0.6 ounces Let ...

Q: q26 The table below lists the frequency of wins for different post positions in a horse race. A post...

A: The null and alternative hypotheses for the test would be: H0: Wins occur with equal frequency in th...

Q: Assume that females have pulse rates that are normally distributed with a mean of mu equals 75.0μ=75...

A: a. The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the me...

Q: A random sample of 92 checking accounts at a bank showed an average daily balance of $311. The stand...

A: GivenSample size (number of accounts) n = 92Sample mean (average daily balance) = $311Population sta...

Q: A student was asked to find a 95% confidence interval for the population proportion of students who ...

A: Click to see the answer

Q: You are interested in finding a 90% confidence interval for the mean number of visits for physical t...

A: Click to see the answer

Q: Stereograms, revisited Because of the skewness of thedistributions of fusion times described in Exer...

A: The data represents the boxplots for the log(fusion times) of two groups, NV and VV. In the boxplot,...

Q: True or false If false, explain briefly. a) We choose the linear model that passes through the most ...

A: a) We choose the linear model that passes through the most data points on the scatterplot: Given sta...

Q: In a study of the accuracy of fast food drive-through orders, Restaurant A had 239 accurate orders a...

A: Click to see the answer

Q: Cattle, part III Suppose the auctioneer in Exercise 19sold a herd of cattle whose minimum weight was...

A: The weights of Angus steers follow normal model with mean 1,152 and standard deviation 84. An auctio...