Question

In: Statistics and Probability

Research by Steelcase suggested that approximately 50% of U.S. workers get interrupted every 11 minutes (and...

Research by Steelcase suggested that approximately 50% of U.S. workers get interrupted every 11 minutes (and take 23 minutes to get back on task). However, Enterpeneur.com conducted a survey of 200 randomly selected U.S. workers and found that 168 said they were interrupted at least every 11 minutes by e-mail, texts, alerts, etc. What does the survey suggest about the Steelcase research?

a.) What is the inherent question of interest here? b.) What might be a reasonable description of the population of interest? c.) what is the relevant sample? d.) what is the random variable being evaluated here? e.) what is the population parameter of interest? f.) what is the parameters corresponding sample statistic? g.) what is an appropriate research hypothesis to consider? h.) what is the corresponding null hypothesis? i.) what is the test statistic used to test these hypothesis? j.) what is the null distribution of this test statistics? k.) what is the decision rule that might be used here? l.) what decision was made with regard to the null hypothesis? m.) what is your conclusion based on the available data? n.) what is the best point estimate of the proportion of the U.S. workers who are interrupted at least every 11 minutes? o.) provide a 95% confidence interval for the proportion of U.S. workers who are interrupted at least every 11 minutes.

Expert Solution

a.) What is the inherent question of interest here?

Interruption of US workers is question of interest.

b.) What might be a reasonable description of the population of interest?

Population of interest = US Workers.

c.) what is the relevant sample?

200 randomly selected U.S. workers

d.) what is the random variable being evaluated here?

Interruption of US workers is the random variable.

e.) what is the population parameter of interest?

population proportion p₀ = 0.5

f.) what is the parameters corresponding sample statistic?

n = 200, r = 168, p = 168/200 = 0.84

g.) what is an appropriate research hypothesis to consider?

H_a : p₀ 0.5

h.) what is the corresponding null hypothesis?

H₀ : p₀ = 0.5

i.) what is the test statistic used to test these hypothesis?

one proportion Z statistic

j.) what is the null distribution of this test statistics?

Considering alpha = 0.05 , null distribution of Z = (-1.96 , 1.96)

k.) what is the decision rule that might be used here?

If test stat is less than -1.96 or greater than 1.96 then reject null hypothesis otherwise fail to reject null hypothesis.

l.) what decision was made with regard to the null hypothesis?

test stat Z = = 9.616

Sine test stat is greater than 1.96 we reject null hypothesis.

m.) what is your conclusion based on the available data?

There is a significant evidence to conclude that the proportion of U.S. workers get interrupted every 11 minutes is significantly different than 0.5.

n.) what is the best point estimate of the proportion of the U.S. workers who are interrupted at least every 11 minutes?

p = 168/200 = 0.84

o.) provide a 95% confidence interval for the proportion of U.S. workers who are interrupted at least every 11 minutes.

95% CI =

p = 0.84, Z_0.025 = 1.96 , n= 200

95% CI = (0.789 , 0891)

orchestra answered 2 years ago

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