An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Does the data provide sufficient evidence to conclude that the number of errors in auditing technique A is greater than the number of errors in auditing technique B at the 0.1 level of significance? Select the [Rejection Region, Decision of Reject (RH₀) or Failure to Reject (FRH₀)]. (Hint: the samples are dependent)

a) [t < -1.4, FRH₀]

b) [z < -1.4 and -z < -1.4, FRH₀]

c) [-t < 1.4 and t < 1.4, RH₀]

d) [t > 1.4, RH₀]

1-

Calculate a) arithmetic mean and b) standard deviation of the sample.

A)

b)

- Represent a classified frequency table. Answer the following questions in this table with column calculations.

Calculate a) arithmetic mean, b) quadratic mean, c) geometric mean, d) corrected standard deviation, e) mode and f) median

a)

b)

c)

d)

e)

f)

Calculate and interpret g) skewness, h) curvature and ı) coefficient of consolidation?

g)

h)

ı)

What is the critical value, of which 90% of all observations have a larger value?

A marketing study was conducted to assess the new bottle design of a popular soft drink. Sixty randomly selected shoppers participated and rated the new design. The data are given below:

34 33 33 29 26 33 28 25 32 33
32 25 27 33 22 27 32 33 32 29
24 30 20 34 31 32 30 35 33 31
32 28 30 31 31 33 29 27 34 31
31 28 33 31 32 28 26 29 32 34
32 30 34 32 30 30 32 31 29 33

a. Explain why we need to construct a frequency distribution and histogram for this data set.
b. Construct a relative frequency distribution and a percent frequency distribution for the bottle design ratings.
c. Construct a cumulative frequency distribution and cumulative percent frequency distribution.

Question text

7-step Hypothesis Testing Problem

Complete the 7 steps in Excel and upload the file here

Two major automobile manufacturers have produced compact cars with the same size engines.We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data show the results of the test.

At the 0.05 level of significance, conduct a 7-step hypothesis test to determine whether there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles.

THE CODE MUST BE PYTHON

superHeroes = {
"MoleculeMan": {
"age": 29,
"secretIdentity": "Dan Jukes",
"superpowers": [
"Radiation Immunity",
"Turning tiny",
"Radiation blast"
]
},
"MadameUppercut": {
"age": 39,
"secretIdentity": "Jane Wilson",
"superpowers": [
"Million tonne punch",
"Damage resistance",
"Superhuman reflexes"
]
},
"EternalFlame": {
"age": 1000,
"secretIdentity": "Unknown",
"superpowers": [
"Immortality",
"Heat Immunity",
"Inferno",
"Teleportation",
"Interdimensional travel"
]
},
"Doomguy": {
"age": 27,
"secretIdentity": "Space Trooper",
"superpowers": [
"Immortality",
"Heat Immunity",
"Teleportation",
"Super Speed",
"Superhuman reflexes"
]
},
"Maui":{
"age": 2352,
"secretIdentity": "Unknown",
"superpowers": [
"Immortality",
"Super Speed"
]
},
"Superwoman":{
"age": 1167,
"secretIdentity": "Lois Lane",
"superpowers": [
"Immortality",
"Super Speed",
"Superhuman reflexes"
]
} ,
  
}

# Question 2 (5 points)
# Output a set containing the ages of all the superheroes.
# Output the name and the age of the youngest superhero.
# Sample output is below.

Set of all ages: {39, 1000, 1167, 2352, 27, 29}
Doomguy is 27 years old.

A) In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

B)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first and last rounds in the tournament.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

The sales manager of a consulting firm hires salespeople based on the personalities of the customers and when assigning customers to sales people. What are the pros and cons of this?

how PetMed will increase its competitive advantage by increasing the acquisition of new customers and increasing sales to loyal customers. What can they do?

A study was conducted to investigate the relationship between maternal smoking during pregnancy and the presence of congenital malformations in the child. Among children who suffer from an abnormality other than Down’s syndrome or an oral cleft, 32.8% have mothers who smoked during pregnancy. You wish to determine if this proportion is the same for those children born with an oral cleft. In a random sample of 27 infants with an oral cleft, 15 had mothers who smoked during pregnancy.

a. What is the estimate of the proportion of infants born with oral clefts whose mothers smoked during pregnancy?

b. Construct a 95% confidence interval for the true population proportion.

c. What are the Null and Alternative Hypotheses of this test?

d. Conduct the test at the 0.05 level of significance.

e. Using Stata, determine the sample size required to have 80% power to detect an alternative of 40% at the 0.01 level of significance.