a light bulb manufacture gaurentees that the mean life of a certain type of bulb is at least 875 hours. A random sample of 40 light bulbs has a mean life of 863 hours with a standard deviation of 50. a=0.04
What is your question?
Work: A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime
What
percentage of light bulb fail to satisfy to guarantee
To determine whether the manufacturer's claim, that the mean life of the bulbs is at least 875 hours, is statistically supported or not, we can perform a hypothesis test using the given information.
Let's set up the null (H0) and alternative (H1) hypotheses:
H0: μ >= 875 (The mean life of the bulbs is at least 875 hours)
H1: μ < 875 (The mean life of the bulbs is less than 875 hours)
To conduct the hypothesis test, we will use a one-sample t-test since the sample size is small (n = 40) and the population standard deviation (σ) is unknown.
First, let's calculate the test statistic.
t = (sample mean - population mean) / (sample standard deviation / √n)
= (863 - 875) / (50 / √40)
= -12 / (50 / √40)
Next, we need to determine the critical value for a significance level of 0.04 (α = 0.04) and degrees of freedom (df = n - 1 = 39).
Since it is a one-tailed test (H1: μ < 875), we will find the critical value using a t-distribution table or a t-distribution calculator.
For a significance level of 0.04 and degrees of freedom (df = 39), the critical value is approximately -1.681.
Now, let's compare the test statistic with the critical value.
If the test statistic is less than the critical value, we reject the null hypothesis (H0). Otherwise, we fail to reject the null hypothesis.
In this case, if the calculated t-value is less than -1.681, we'll reject the null hypothesis and conclude that there is enough evidence to support that the mean life of the bulbs is less than 875 hours.
Note: The calculations provided are based on the assumption that the sample is representative of the population, and the data is collected randomly and independently.
Please substitute the values mentioned in the calculations to get the precise result.