it is claimed that 95% of teenagers who have a cell phone never leave home without it. to investigate this…

it is claimed that 95% of teenagers who have a cell phone never leave home without it. to investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. it was discovered that 273 of the teenagers in the sample never leave home without their cell phone. one question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. what are the values of the test statistic and p - value for this test? find the z - table here. z = 3.18, p - value = 0.0007 z = - 3.18, p - value = 0.0007 z = 3.18, p - value = 0.0014 z = - 3.18, p - value = 0.0014

it is claimed that 95% of teenagers who have a cell phone never leave home without it. to investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. it was discovered that 273 of the teenagers in the sample never leave home without their cell phone. one question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. what are the values of the test statistic and p - value for this test? find the z - table here. z = 3.18, p - value = 0.0007 z = - 3.18, p - value = 0.0007 z = 3.18, p - value = 0.0014 z = - 3.18, p - value = 0.0014

Answer

Explanation:

Step1: Calculate the sample proportion

The sample proportion (\hat{p}=\frac{273}{300}=0.91)

Step2: Calculate the test statistic (z)

The formula for the test statistic in a one - sample proportion test is (z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}) where (p_0 = 0.95), (n=300), (\hat{p}=0.91) [ \begin{align*} z&=\frac{0.91 - 0.95}{\sqrt{\frac{0.95\times(1 - 0.95)}{300}}}\ &=\frac{- 0.04}{\sqrt{\frac{0.95\times0.05}{300}}}\ &=\frac{-0.04}{\sqrt{\frac{0.0475}{300}}}\ &=\frac{-0.04}{\sqrt{0.00015833\cdots}}\ &=\frac{-0.04}{0.0126}\ &=- 3.18 \end{align*} ]

Step3: Calculate the (P -)value

Since this is a left - tailed test ((H_1:p\lt0.95)), the (P -)value is (P(Z\lt z)) where (z=-3.18) Looking up (z = - 3.18) in the standard normal ((z -)) table, the (P -)value is (0.0007)

Answer:

(z=-3.18), (P -)value (=0.0007) (the second option)