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?