DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime x-805 hours with a standard deviation s 158 hours. Using the hypotheses H0: μ = 904 vs Ha: μ < 904, find the P-value and state your conclusion. Use a significance level of 0.05.

1. P-value 0.039, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours

2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.

3. P-value 0.079, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.

4. P-value0.079, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours

Question

Mathematics

Geovanni Deleon

17 January, 20:05

DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime x-805 hours with a standard deviation s 158 hours. Using the hypotheses H0: μ = 904 vs Ha: μ < 904, find the P-value and state your conclusion. Use a significance level of 0.05.

1. P-value 0.039, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours

2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.

3. P-value 0.079, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.

4. P-value0.079, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours

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Answers (1)

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Shayla Stone · Answer 1

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: μ = 904

For the alternative hypothesis,

Ha: μ < 904

This is a left tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 10,

Degrees of freedom, df = n - 1 = 10 - 1 = 9

t = (x - µ) / (s/√n)

Where

x = sample mean = 805

µ = population mean = 904

s = samples standard deviation = 158

t = (805 - 904) / (158/√10) = - 1.98

We would determine the p value using the t test calculator. It becomes

p = 0.039

Since alpha, 0.05 > than the p value, 0.03953, then we would reject the null hypothesis. Therefore, the correct option is:

2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.