Calculating Probability of Cars' Expected Speed with Hypothesis Testing

[superwolf]

If $$\sigma = 10 km/h$$ and $$\mu = 74 km/t$$, find the probability that we when measuring the speed of 12 random cars can conclude that the expected speed of the cars is less than 77 km/h. Use $$\alpha$$=0.05 level of significance.

$$z = \frac{\bar{x}-\mu_0}{\sigma / \sqrt{n}} = \frac{77-74}{10/\sqrt{12}}=1.039$$

Am I on the right track?

 

[Pyrrhus]

You should always state your hypothesis and then process to do the test statistic.

Also a Z statistic in this case, might be appropriate is the underlying population distribution is known to be normal. For this case maybe you can use it safely, because car speeds are usually normally distributed if the the simple random samplings were done correctly.

You should also state your conclusion, Do you Reject or Fail to Reject the null?

 

[superwolf]

$$H_0: v=77$$
$$H_1: v<77$$

 

[superwolf]

$$H_0:\mu =77$$

$$H_1:\mu <77$$

$$z_{observed} = 1.039$$

What should I do now?

 

[Mark44]

Since you're dealing with a normal distribution, the probability of your null hypothesis is zero. Also, your null and alternate hypotheses should include all possibilities -- what if v > 77?

From the wording of the problem I think these are your hypotheses:
H₀: v < 77
H₁: v >= 77

With things set up this way, your test would be a one-tailed test.