Question

Is there a significant difference between the typing speed of male and female secretaries? A recent test produced the following data: 36 male secretaries average 70 wordds/min with standard diviation of 10 words/ min, amd 30 female secretaties avearge 78 words/min with a standard diviation of 10 words/min?

1. State the null hpothesis and alternative hyphothesis?

2. Find the test statistic?

3. If the type of I-error a=0.005 , find the critical value(s) and draw the rejection region(s)?

4. Base on the type of I-error a, given above, what is your cnclusion ?

Answer 1

1. State the null hpothesis and alternative hyphothesis?

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 is population mean words/min of male

mu2 is population mean words/min of female

Assume alpha = level of significance = 0.005

Given that,

Sample size of male (n1) = 36

Sample mean of male (X1bar) = 70 words/min

Sample standard deviation (s1) = 10 words/min

Sample size of female (n2) = 30

Sample mean for female (X2bar) = 78 words/min

Sample standard deviation (s2) = 10 words/min

This is the problem of two sample t-test assuming equal variances.

We can do this test in MINITAB.

steps :

STAT --> Basic statistics --> Two-Sample t for the mean --> Summarized data --> Input all the values --> Options --> COnfidence level : 99.5 --> Hypothesized difference : 0.0 --> ALternative hypothesis : not equal --> Assume equal variances --> ok --> ok

————— 20-06-2018 09:32:02 ————————————————————

Welcome to Minitab, press F1 for help.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 36 70.0 10.0 1.7
2 30 78.0 10.0 1.8

Difference = ? (1) - ? (2)
Estimate for difference: -8.00
99.5% CI for difference: (-15.19, -0.81)
T-Test of difference = 0 (vs ?): T-Value = -3.24 P-Value = 0.002 DF = 64
Both use Pooled StDev = 10.0000

3. If the type of I-error a=0.005 , find the critical value(s) and draw the rejection region(s)?

Critical value for a = 0.005 is,

Critical value = 2.908

4. Base on the type of I-error a, given above, what is your conclusion ?

Test statistic = -3.24

P-value = 0.002

P-value < alpha and Test statistic > critical value

Reject H0 at 0.005 level of significance.

COnclusion : There is sufficient evidence to say that there a significant difference between the typing speed of male and female secretaries.