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we would like to conduct a hypothesis testing to see if mean vehicle speed at a particular off-ramp on a highway segment is 45 mph. we have collected vehicle speed data for 60 vehicles to create a sample. the mean speed for these 60 observations is 46.5 mph. assuming the sample standard deviation is 4.1, conduct a hypothesis testing to see if population mean speed on this off-ramp is 45 mph at a 95% confidence level. what is ? group of answer choices

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Answer: The test statistic ? is 3.17.

Explanation:

To conduct a hypothesis testing to see if the population mean speed on the off-ramp is 45 mph at a 95% confidence level, we need to set up the null and alternative hypotheses:

Null hypothesis: The population mean speed on the off-ramp is 45 mph (μ = 45)

Alternative hypothesis: The population mean speed on the off-ramp is not 45 mph (μ ≠ 45)

We can use a two-tailed t-test since we do not have any prior knowledge about the direction of the difference.

Next, we need to calculate the test statistic:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

t = (46.5 - 45) / (4.1 / sqrt(60))

t = 3.17

The degrees of freedom (df) for this test is (n - 1) = 59. We can find the critical value using a t-table or a t-distribution calculator for a 95% confidence level with df = 59:

t_critical = ±2.002

Since our calculated t-value (3.17) is outside the range of the critical values (-2.002, 2.002), we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean speed on the off-ramp is not 45 mph at a 95% confidence level.

Answer: The test statistic ? is 3.17.