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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. Are the results from a few years
ago likely to be valid today?
Step 1. Claim: fewer than half of all households have a high-definition
television (p < 0.5).
Step 2: p ≥ 0.5
Step 3: H0: p = 0.5; H1: p < 0.5
Step 4: a = 0.01
Step 5: Test statistic is a normal distribution.
Step 6: P-value method
n: 1500, p̂: 0.47, p: 0.5, q: 0.5
0.47−0.5
−0.03
√
Z= 0.5∗0.5 = 0.012909944 =-2.32
1500
P value (-2.32): 0.010
Conclusion: The p-value, 0.010, is equal to the significance level, 0.01, we
have rejected the null hypothesis. There is insufficient evidence to conclude
that half of all households have a high-definition TV.
As for the second question, without more information, it is difficult to say
whether the outcomes from a few years ago are still applicable now. It's
likely that the percentage of homes with high-definition televisions has gone
up, down, or stayed the same throughout time. A new poll is needed to
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. Are the results from a few years
ago likely to be valid today?
Step 1. Claim: fewer than half of all households have a high-definition
television (p < 0.5).
Step 2: p ≥ 0.5
Step 3: H0: p = 0.5; H1: p < 0.5
Step 4: a = 0.01
Step 5: Test statistic is a normal distribution.
Step 6: P-value method
n: 1500, p̂: 0.47, p: 0.5, q: 0.5
0.47−0.5
−0.03
√
Z= 0.5∗0.5 = 0.012909944 =-2.32
1500
P value (-2.32): 0.010
Conclusion: The p-value, 0.010, is equal to the significance level, 0.01, we
have rejected the null hypothesis. There is insufficient evidence to conclude
that half of all households have a high-definition TV.
As for the second question, without more information, it is difficult to say
whether the outcomes from a few years ago are still applicable now. It's
likely that the percentage of homes with high-definition televisions has gone
up, down, or stayed the same throughout time. A new poll is needed to
