1. A certain brand of Green Energy light bulbs was advertised as having an average illumination life-span of 2,500 hours. A random sample of 50 bulbs burned out with a mean life-span of 2,470 hours and a sample standard deviation of 140 hours. With a 0.05 level of significance, is the sample mean less than the advertised mean?
2. Given the following data from two independent samples, conduct a one-tailed hypothesis test to determine if the first sample mean is larger than the second sample mean, given a 0.05 level of significance.
n1 = 55 n2 = 46
xbar1= 72 xbar2 = 62
s1=15 s2 = 12
3. A test was conducted to determine whether gender of a spokesperson affected the likelihood that consumers would prefer a new vacuum cleaner. A survey of consumers at a trade show employing a female spokesperson determined that 78 out of 200 customers preferred the product, while 56 of 180 customers preferred the product when a male spokesperson was employed. At the 0.05 level of significance, do the samples provide sufficient evidence to indicate that on the average, fewer consumers prefer a new product when the spokesperson is male?
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The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.