manufacturer claims that the mean lifetime,  μ , of its light bulbs is  53  months. The standard deviation of these lifetimes is  4  months. Eleven bulbs are selected at random, and their mean lifetime is found to be  56  months. Assume that the population is normally distributed. Can we conclude, at the  0.05  level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from  53  months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis  H0  and the alternative hypothesis  H1 . H0: H1: (b) Determine the type of test statistic to use.   ▼(Choose one)   (c) Find the value of the test statistic. (Round to three or more decimal places.)   (d) Find the two critical values. (Round to three or more decimal places.) and (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from  53  months?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.