A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 701.6 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic?

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower then 720 hours at 5% of signficance.  

Step-by-step explanation:

Data given and notation    

represent the sample mean

represent the population standard deviation    

sample size    

represent the value that we want to test  

represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)    

represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean is at least 720 hours :    

Null hypothesis:    

Alternative hypothesis:    

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:    

(1)    

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

P-value    

Since is a left tailed test the p value would be:    

Conclusion    

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower then 720 hours at 5% of signficance.    

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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