Question

The mean annual tuition and fees for a sample of 14 private colleges in California was $37,900 with a standard deviation of $7,200. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude at the 0.01 significance level that the mean tuition and fees for private institutions in California differs from $35,000

Answer 1

Answer:

Z_{0.005}>Z H₀ is wrong and other is correct. IT means $35000 is not mean value.

Step-by-step explanation:

Two hypothesis:

H₀=$35,000

Hₐ≠$35,000

Test Formula:

$Z=\frac{(X-u)}{\frac{S}{\sqrt{n} } }$

Where:

X is the mean value=$37,900

u is the value with 0.01 significance=$35000

S is the standard deviation

n is the sample size

$Z=\frac{(37900-35000)}{\frac{7200}{\sqrt{14} } }$

Z=1.507

Z with 0.01 significance:

0.01/2=0.005=0.05%

Degrees of freedom=14-1=13

From t distribution table at 0.05% and 13 dof:

$Z_{0.005}$=4.221

So

Z_{0.005}>Z H₀ is wrong and other is correct. IT means $35000 is not mean value.