Question

Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores:

Grades	73.5	68.4	65	65	63.9	68.4	64.3	66.5	61.9	69

Test grades are believed to be normally distributed.

Use a significance level of 5%.

1. State the standard error of the sample means:  (Round to four decimal places.)
2. State the test statistic: t=t=  (Round to four decimal places.)
3. State the p-value

Answer 1

Solution:

The null and alternative hypothesis are

H₀ : = 65 vs H₁ : > 65

n = 10

73.5,68.4,65,65,63.9,68.4,64.3,64.3,66.5,61.9,69

Using calculator ,

Sample mean = 66.381818181818

Sample standard deviation s = 3.2313520952747

A)

Standard error = =   = 1.0218

Standard error = 1.0218

B)

Sample mean = 66.381818181818

Since population SD is unknown,we use t test.

The test statistics t is given by ..

t =  

= (66.381818181818 - 65)/(3.2313520952747/n)

= 1.3523

t = 1.3523

C)

Observe the alternative hypothesis H₁ : > 65

> sign , so RIGHT TAILED TEST (One tailed right sided)

n = 10

So , df = n - 1 = 10 - 1 = 9

Using df = 9 , t = 1.3523 , One tailed test

p value = 0.1046