1. In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the consumer electronics association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high-definition television. Is the result from a few years ago likely to be valid today?
"H_0: p_0 = 0.5 \\\\\n\nH_1: p_0 < 0.5 \\\\\n\n\u03b1=0.01 \\\\\n\nN= 1500 \\\\\n\np = 0.47"
Test-statistic
"Z = \\frac{p-p_0}{\\sqrt{\\frac{p_0(1-p_0)}{N}}} \\\\\n\nZ = \\frac{0.47-0.5}{\\sqrt{\\frac{0.5(1-0.5)}{1500}}} \\\\\n\nZ = \\frac{-0.03}{\\sqrt{\\frac{0.5 \\times 0.5}{1500}}} \\\\\n\nZ = -2.324"
At α=0.01 the critical value for a left-tailed test is "Z_c = -2.326"
Since "Z>Z_c" the null hypothesis is accepted.
There is NOT enough evidence to claim that fewer than half of all households have a high-definition television at 0.01 level of significance.
If the data and claim are the same in few years ago, the results likely to be valid today.
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