Provide examples of how the t test and ANOVA could be used to compare means within your work environment or domain of interest. Discuss the appropriateness of using the t test versus ANOVA.

A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is x=820 and the sample standard deviation is s=25. (Round all answers to 3 decimal places)

(a) Construct an interval estimate of u with 99% confidence

(b) Construct an interval estimate of u with 99% confidence, assuming that s=50

(c) Construct an interval estimate of u with 99% confidence, assuming that s=100

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation a=.000672 mm. Assume a random sample of 56 sheets of metal resulted in an x=.2737 mm

Calculate the 98 percent confidence interval for the true mean metal thickness

Interval is from ? to ? Round to 4 decimal places

Use the sample information x=44, a=6, n=17 to calculate the following confidence intervals for u assuming the sample is from a normal population

(a) 90% confidence interval is ? to ?

(b) 95% confidence interval is ? to ?

(c) 99% confidence interval is ? to ?

A pizza restaurant sold 24 cheese pizzas and 16 specialty pizzas for a particular day. 14 of the cheese pizzas were sold to familiies with young children. 6 of the specialty pizzas were sold to familiies with young children. If a pizza was selected at random, what is the probability it was a specialty pizza or a pizza sold to a family without young children?

Select one:

a. 20/40 = 1/2

b. 26/40 = 13/20

c. 6/40 = 3/20

d. 16/40 = 2/5

Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.71 million households with a sample standard deviation of 0.57 million family units. Over the same 12 months Spotify was used by an average of 2.24 million families with a sample standard deviation of 0.31 million. Assume the population standard deviations are not the same.

Using a significance level of 0.10, test the hypothesis of no difference in the mean number of households picking either service

a)Find the degrees of freedom for unequal variance test. (Round down your answer to nearest whole number.)

b)State the decision rule for 0.10 significance level: H₀: μ_Apple = μ_Spotify; H₁: μ_Apple ≠ μ_Spotify. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

c)Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

d)Test the hypothesis of no difference in the mean number of households picking either variety of service to download songs.

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets.

At the 0.100 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

1. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

2. Compute the test statistic. (Round your answer to 2 decimal places.)

3. State your decision about the null hypothesis.

- Show an example of an observational study that looks or sounds scientific, with the reference.

1 - Explain what makes the study look or seem scientific.

2 - Explain what the problems with the study are and some of the possible ramifications if you were to accept the claim(s) being made as true.

3 - Briefly discuss what might happen if many people accepted the claim(s) being made as true.

A problem statement is an integral part of the research. Elaborate on the meanings of “problem” according to pure research and applied research.

Sub: Test on Hypothesis (Maths)

Kindly solve the sum and provide the detailed step by step method:-

A random sample of size 15 has 50 as mean, the sum of the squares of the deviation taken from mean is 130.Can this sample be regarded as taken from the population having 53 as mean?. Obtain 95% and 99% confidence limits of the mean for the population.

A motorist goes for a drive, keeping the reading on the speedometer at a constant value of 40 km/h. The speedometer is assumed to be accurate to +- 2 km/h. At the end of the day he wants to know how far he has travelled, but unfortunately he forgot to look at the distance indicator when he set out. He thinks that he drove for four hours, give or take a quarter of an hour. Estimate how far he travelled and assign an error to your result.

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 69 and estimated standard deviation σ = 44. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places

b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

The probability distribution of x is approximately normal with μ_x = 69 and σ_x = 44.

The probability distribution of x is not normal.  

   The probability distribution of x is approximately normal with μ_x = 69 and σ_x = 31.11.

The probability distribution of x is approximately normal with μ_x = 69 and σ_x = 22.00.

What is the probability that x < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of the grape-growing region—called the ‘‘terroir.’’ The Economic Journal (May 2008) published an empirical study of the factors that yield a quality Bordeaux wine. A quantitative measure of wine quality (y) was modeled as a function of several qualitative independent variables, including grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

a. Create the appropriate dummy variables for each of the qualitative independent variables.

b. Write a model for wine quality (y) as a function of grape-picking method. Interpret the β’s in the model.

c. Write a model for wine quality (y) as a function of soil type. Interpret the β’s in the model.

d. Write a model for wine quality (y) as a function of slope orientation. Interpret the β’s in the model.

e. Write an interaction model relating wine quality to the two qualitative independent variables; grape-picking method (manual or automated) and soil type (clay, gravel, or sand). Let ‘‘automated’’ and ‘‘sand’’ represent the base levels for the two variables, respectively.

f. Interpret the value of ?0 in the model.

g. In terms of the β’s, what is the mean quality of wine produced from grapes picked manually from clay soil?

h. In terms of the β’s, what is the difference between the mean quality of wine produced from grap

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 333 people living in East Vancouver and finds that 36 have recently had the flu.

For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu.

A. 10.81% (36/333) of East Vancouver residents have recently had the flu. true/ false

B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 36/333. true/false

C. If another random sample of 333 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 36/333. true/false

D. If many random samples of 333 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of East Vancouver residents who have recently had the flu. true/false

E. If many random samples of 333 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value 36/333. true/false

Part 2

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 340 people living in East Vancouver and finds that 33 have recently had the flu.

Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps.

Sample Size =

in the medical trial context, define the term of
research misconduct/fraud