A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique,
862862
births consisted of
448448
baby girls and
414414
baby boys. In analyzing these results, assume that boys and girls are equally likely.
a. Find the probability of getting exactly
448448
girls in
862862
births.
b. Find the probability of getting
448448
or more girls in
862862
births. If boys and girls are equally likely, is
448448
girls in
862862
births unusually high?
c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)?
d. Based on the results, does it appear that the gender-selection technique is effective?
In: Math
You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let r.v. X represent the number of correct responses on the exam.
(a). Specify the probability distribution of X.
(b. What is your expected number of correct responses?
(c). What are the values of the variance and standard deviation of X?
(d). What is the probability that you will get exactly the expected number of correct responses?
In: Math
The numbers of online applications from simple random samples of college applications for 2003 and for the 2009 were taken. In 2003, out of 312 applications, 97 of them were completed online. In 2009, out of 316 applications, 78 of them were completed online. Test the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003 at the .10 significance level.
Claim: Select an answer u 1 ≤ u 2 u 1 = u 2 p 1 < p 2 u 1
< u 2 p 1 ≤ p 2 p 1≠p 2 u 1 > u 2 p 1 = p 2 u 1≠u 2 u 1 ≥ u 2
p 1 ≥ p 2 p 1 > p 2 which corresponds to Select an
answer H1: u 1 > u 2 H0: u 1 ≤ u 2 H1: u 1 < u 2 H0: p 1 = p
2 H1: p 1 < p 2 H1: p 1 > p 2 H1: u 1≠u 2 H0: p 1 ≤ p 2 H1: p
1≠p 2 H0: p 1≠p 2
Opposite: Select an answer u 1 = u 2 p 1 > p 2 u 1 < u 2 p
1 ≤ p 2 p 1≠p 2 u 1 ≥ u 2 u 1 ≤ u 2 u 1 > u 2 p 1 ≥ p 2 p 1 = p
2 u 1≠u 2 p 1 < p 2 which corresponds to Select an
answer H1: u 1 <= u 2 H0: u 1 > u 2 H1: u 1 ≥ u 2 H0: u 1≠u 2
H1: u 1 = u 2 H0: p 1 = p 2 H1: p 1 > p 2 H0: p 1≠p 2 H0: p 1 ≤
p 2 H1: p 1≠p 2 H1: p 1 < p 2
The test is: Select an answer /right-tailed / two-tailed /
left-tailed
The test statistic is: z = Select an answer 1.79 / 1.95 / 1.47 / 2.28 / 2.05 (to 2 decimals)
Based on this we: Fail to reject the null hypothesis / Accept
the null hypothesis / Reject the null hypothesis / Cannot determine
anything
Conclusion There Select an answer ( does / does not ) appear to be enough evidence to support the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003.
The critical value is: z a/ 2= ±± Select an answer / 1.64 / 1.44 / 1.64 / 1.28 / 1.15 (to 2 decimals)
In: Math
33) Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.
| 9.3 | 9.0 | 10.5 | 9.1 | 9.4 | 9.8 | 10.0 | 9.9 | 11.2 | 12.1 |
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)
| x = | mg/dl |
| s = | mg/dl |
(b) Find a 99.9% confidence interval for the population mean of
total calcium in this patient's blood. (Round your answer to two
decimal places.)
| lower limit | mg/dl |
| upper limit | mg/dl |
In: Math
A noted psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence?
In: Math
An experiment is picking a card from a fair deck. a.) What is the probability of picking a Jack given that the card is a face card? b.) What is the probability of picking a heart given that the card is a three? c.) What is the probability of picking a red card given that the card is an ace? d.) Are the events Jack and face card independent events? Why or why not? e.) Are the events red card and ace independent events? Why or why not?
In: Math
7. Circus
A traveling circus has found that its average attendance per performance is 6000 people with a
standard deviation of 1500. Assume that attendance is normally distributed.
a)
Suppose that a town asks the circus to come, but the only available site in town holds a
maximum of 8000 people. What is the probability that this site will reach capacity?
b)
If the circus loses money on 20% of its performances, what attendance must it have to
break even for a performance?
In: Math
For the data below construct a 95% confidence interval for the population mean.
53.4 51.6 48.0 49.8 52.8 51.8 48.8 43.4 48.2 51.8 54.6 53.8 54.6 49.6 47.2
In: Math
The president of Amalgamated Retailers International, Sam Peterson, has asked for your assistance in studying the market penetration for the company’s new cell phone. You are asked to determine if the market share is equal to the company’s claim of 35%. You obtain a random sample of potential customers from the area. The sample indicates that 258 out of a total sample of 800 indicate they will purchase from Amalgamated
[a] Using a probability of error , test the hypothesis that the market share equals the company’s claim of 35% versus the hypothesis that the market share is not equal to the company’s claim.
[b] Using a probability of error , test the hypothesis that the market share equals the company’s claim of 35% versus the hypothesis that the market share is less than the company’s claim.
Please Include:
In: Math
A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.
| Group-1 | Group-2 | Group-3 | Group-4 |
|---|---|---|---|
| 73.5 | 76.7 | 75 | 65.7 |
| 81 | 66.4 | 77.8 | 50.5 |
| 61.8 | 60.3 | 66.7 | 83 |
| 69.5 | 81 | 70.3 | 81.4 |
| 77.4 | 57.9 | 77.7 | 74.9 |
| 91.2 | 59.2 | 68.1 | 82.9 |
| 70.6 | 67.9 | 83.5 | 85.4 |
| 64 | 54.9 | 87.8 | 63.6 |
| 73.2 | 63.2 | 80.6 | 67.6 |
| 77.7 | 69.8 | 58.9 | 73.6 |
| 73.6 | 69.1 | 86.7 | 81.5 |
| 77.2 | 51.8 | 74.7 | 80.5 |
| 54 | 60.5 | 66.9 | 71.8 |
| 65.4 | 55.4 | 76.7 | 68.1 |
| 77.8 | 68.2 | 76.3 | 55.8 |
| 81.6 | 64.8 | 69.5 | 70.4 |
First, run an ANOVA with this data and fill in the summary table.
(Report P-values accurate to 4 decimal places and all
other values accurate to 3 decimal places.
| Source | SS | df | MS | F-ratio | P-value |
|---|---|---|---|---|---|
| Between | |||||
| Within |
To follow-up, the professor decides to use the Tukey-Kramer method
to test all possible pairwise contrasts.
What is the Q critical value for the Tukey-Kramer critical range
(alpha=0.01)?
Use the website link in your notes
(http://davidmlane.com/hyperstat/sr_table.html) to locate the Q
critical value to 4 decimal places.
Q =
Using the critical value above, compute the critical range and then
determine which pairwise comparisons are statistically
significant?
In: Math
Census data for a city indicate that 29.0% of the under-18 population is white, 26.2% black, 33.2% Latino, 9.5% Asian, and 2.1% other ethnicities. The city points out that of 25,577 police officers, 64.8% are white,14.5% black, 19.1% Latino, 1.4% Asian, and the remaining are other ethnicities. Do the police officers reflect the ethnic composition of the city's youth? Complete parts a through e below.
A) What is the appropriate test?
B) What is the null and alternative hypothesis?
C) What is the chi squared test statistic
D) what is the p value
In: Math
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 220 customers on the number of hours cars are parked and the amount they are charged.
| Number of Hours | Frequency | Amount Charged | |||
| 1 | 15 | $ | 2 | ||
| 2 | 36 | 6 | |||
| 3 | 53 | 9 | |||
| 4 | 40 | 13 | |||
| 5 | 20 | 14 | |||
| 6 | 11 | 16 | |||
| 7 | 9 | 18 | |||
| 8 | 36 | 22 | |||
| 220 | |||||
|
|||||
In: Math
According to actuarial tables, life spans in the United States are approximately normally distributed with a mean of about 75 years and a standard deviation of about 16 years.
1) Find the probability that a randomly selected person lives between 60 less than 90 years.
2) Find the probability that a randomly selected person lives less than 50 years or more than 100 years.
3) Find the probability that a randomly selected person lives exactly 75 years.
4) What age is considered to be the 99th percentile?
5) What age is considered to be in the 10th percentile?
In: Math
For each of the questions below, a histogram is described. Indicate in each case whether, in view of the Central Limit Theorem, you can be confident that the histogram would look like approximately a bell-shaped (normal) curve, and give a brief explanation why (one sentence is probably sufficient).
1. The price of one gallon of gasoline at a particular gas station is recorded every day of the year, and the 365 values are plotted in a histogram.
2. Two hundred students in a statistics class each flip a coin 40 times and record the number of heads. The numbers of heads are plotted in a histogram.
3. Two hundred students in a statistics each roll a die 60 times and record the sum of the numbers they got on the 60 rolls. They make a histogram of the 200 sums.
4. One thousand randomly chosen people report their annual salaries, and these salaries are plotted in a histogram.
5. The day before an election, fifty different polling organizations each sample 2000 people and record the percentage who say they will vote for the Democratic candidate. The 50 values are plotted in a histogram.
6. The fifty polling organizations also record the average age of the 2000 people in their sample, and the 50 averages are plotted in a histogram.
7. One hundred batteries are tested, and the lifetimes of the batteries are plotted in a histogram.
In: Math
We must show our work
6. Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 90 randomly sampled television viewers, 18 indicated that they asked their physician about using a prescription drug they saw advertised on TV. Develop a 90% confidence interval for the proportion of viewers who discussed a drug seen on TV with their physician. (Hint: Review section Confidence Interval for a Population Proportion)
In: Math