Question

Ive been given the following numbers 42, 47, 50, 49, 32 to show speed of cars driving down a particular street.

How do I test the null hypothesis H0 : μ = 62.6 against the alternative hypothesis H1 : μ > 62.6 using a 10% significance level, where μ is the expected value of the speed of all cars driving down the street.

State any assumptions that you needed to make in order for your answers to be valid.

also does the CLT apply to any sample over 25? Thanks

Answer 1

Step 1:

Ho:  μ = 62.6

H1 : μ > 62.6

Step 2:

Sample mean = 220/ 5 = 44

data	data-mean	(data - mean)2
42	-2	4
47	3	9
50	6	36
49	5	25
32	-12	144

Assuming that the data is normally distributed, also as the population sd is not given, we will calculate t stat.

Step 3:

df = 5-1 = 4

= 0.10

t critical (right tailed test) = 1.53320627

As t stat does not fall in the rejection area, we fail to reject the Null hypothesis.

According to the  Central Limit Theorem the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.