A new light bulb is being considered for use in an office. It is decided that the new light bulb will be used only if it has amean lifetime more than 500 hours. A random sample of50 lightbulbsis selected and placed on lifetime test in which n= 50 lifetimes were obtained. The sample mean and sample standard deviation obtained in the lifetime test are502hours and22hours, respectively.

Is it sufficient sample evidence to conclude that the mean lifetime of a new light bulb ismore than500hours and it will be used in an office?

Test the appropriate hypothesis at predetermined level of significance =0.05. Usep - value approach.

a. State null and research hypotheses:

₀H:___________________

₁H:___________________

b. Find the observed value of test statistic. The observed value of test statistic is_.z_obs=__________________________ (Keep 2 digits after decimal point in the expression for observed value of test statistics.)

c. Find p -value of the test.

p -value of the test is equal to _________________

d. Insert the words "to reject"or "not to reject" into the following statement.

Your conclusion is __________________________ null hypothesis.

Please help with this Practice Question.