Question

The population of Mosquito has an unknown mean lifespan μ with standard deviation σ = 0.55 days. A) A sample of 23 mosquito has a mean lifespan of 6.5 days. Construct a 87 % confidence interval to estimate the mean lifespan μ of the mosquito population. Round to 4 decimal places.) The interval: 6.5 (Round E to 2 decimal places) The interval in traditional format: ( B) For the same sample of 23 mosquito with mean lifespan of 6 5 days, construct a 95 % confidence interval to estimate the mean life span μ of the mosquito population. Round to 4 decimal places.) The interval: 6.5 (Round E to 2 decimal places) The interval in traditional format: C) A sample of 300 mosquito also has a mean lifespan of 6.5 days. Construct a 87 % confidence interval to estimate the mean lifespan μ of the mosquito population. (Round to 4 decimal places.) The interval: 6.5 Round E to 2 decimal places) The interval in traditional format: ( D) A sample of 399 mosquito also has a mean lifespan of 6.5 days. Construct a 95 % confidence interval to estimate the mean lifespan μ of the mosquito population. (Round to 4 decimal places.) The interval: 6.5 Round E to 2 decimal places) The interval in traditional format

Answer 1

The formula for estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

Note the notation has been changed for mean and standard deviation please consider

a)

M = 6.5
Z = 1.51
s_M = √(0.55²/23) = 0.11

μ = M ± Z(s_M)
μ = 6.5 ± 1.51*0.11
μ = 6.5 ± 0.17

87% CI [6.33, 6..67].

b)Calculation

M = 6.5
Z = 1.96
s_M = √(0.55²/23) = 0.11

μ = M ± Z(s_M)
μ = 6.5 ± 1.96*0.11
μ = 6.5 ± 0.22

95% CI [6.28, 6.73].

c)M = 6.5
Z = 1.51
s_M = √(0.55²/300) = 0.03

μ = M ± Z(s_M)
μ = 6.5 ± 1.51*0.03
μ = 6.5 ± 0.05

CI= {6.45, 6.55}

d) Calculation

M = 6.5
Z = 1.96
s_M = √(0.55²/399) = 0.03

μ = M ± Z(s_M)
μ = 6.5 ± 1.96*0.03
μ = 6.5 ± 0.05

95% CI [6.45, 6.55].

The Z value is calculated using Z table shown below