Question

1.) Use the given information below to answer the following questions.

a.) A sample of 25 lightbulbs was taken and it was found that the mean lifetime of a certain bulb for a movie projector is 520 hours with a standard deviation of 50 hours. The standing assumption of the manufacturing company is that the lifetime of this type pf bulb is no more than 500 hours. Assume a normal distribution. Does the data support the company’s claim at a level of significance of α = .10? Provide supporting explanation and show your work.

b.) A sample was taken of four dog treats and it was found that the mean grams of fat is 11 g with a standard deviation of 1.8 g. The standing assumption of the dog treat manufacturer is that the treats have 10 g of fat. Assume a normal distribution. Does the data support the company’s claim at a level of significance of α = .05? Provide supporting explanation and show your work.

Answer 1

#1.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ <= 500
Alternative Hypothesis, Ha: μ > 500

Rejection Region
This is right tailed test, for α = 0.1 and df = 24
Critical value of t is 1.3178.
Hence reject H0 if t > 1.3178

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (520 - 500)/(50/sqrt(25))
t = 2

P-value Approach
P-value = 0.0285

As P-value < 0.1, reject the null hypothesis.

Data does not support the claim

#2.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10
Alternative Hypothesis, Ha: μ ≠ 10

Rejection Region
This is two tailed test, for α = 0.05 and df = 3
Critical value of t are -3.1824 and 3.1824.
Hence reject H0 if t < -3.1824 or t > 3.1824

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (11 - 10)/(1.8/sqrt(4))
t = 1.111

P-value Approach
P-value = 0.3476

As P-value >= 0.05, fail to reject null hypothesis.

The data supports the claim