Question

PLEASE ANSWER ALL PARTS

The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of four English courses with a standard deviation of 0.8. The females took an average of five English courses with a standard deviation of 1.1. Are the means statistically the same? (Use

? = 0.05)

PART A State the null hypothesis.

Part B  State the alternative hypothesis.   

Part C Choose a choice

In words, state what your random variable X_M ? X_F represents.

1. X_M ? X_F represents the difference in number of English courses taken by males and females.

2. X_M ? X_Frepresents the mean number of English courses taken by males and females.   

3.X_M ? X_F represents the difference in the mean number of English courses taken by males and females.

4.X_M ? X_F represents the mean difference in the number of English courses taken by males and females.

Part D

State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom. Round your answer to two decimal places.)

_______

Part E

What is the p-value? (Round your answer to four decimal places.) ____________
Explain what the p-value means for this problem.

Part G

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? = ____

(ii) Decision: Choose Choice 1 or 2

1.reject the null hypothesis

2. do not reject the null hypothesis    

(iii) Reason for decision: Choose Choice 1,2,3, or 4

1. Since p-value > ?, we reject the null hypothesis.

2.Since p-value < ?, we reject the null hypothesis.   

3. Since p-value > ?, we do not reject the null hypothesis.

4. Since p-value < ?, we do not reject the null hypothesis.

(iv) Conclusion:Choose Choice 1, or 2

1.There is sufficient evidence to show that the mean number of English courses that males and females take is different.

2. There is not sufficient evidence to show that the mean number of English courses that males and females take is different.   

part H choose choice 1 2 3 4

Explain how you determined which distribution to use.

1. The standard normal distribution will be used because the samples involve the difference in proportions.

2. The t-distribution will be used because the samples are independent and the population standard deviation is not known.    

3. The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

4. The t-distribution will be used because the samples are dependent.

Answer 1

PART A State the null hypothesis.

H0: XM - XF = 0

Part B  State the alternative hypothesis.   

H0: XM - XF $\ne$ 0

Part C Choose a choice

In words, state what your random variable XM ? XF represents.

3.XM - XF represents the difference in the mean number of English courses taken by males and females.

Part D

As, the population standard deviation for XM and XF can be different, the distribution to be used for the test is t distribution.

The  standard error (SE) of the sampling distribution.

SE = sqrt[ (s1²/n1) + (s2²/n2) ]

= sqrt[ (0.8²/29) + (1.1²/16) ] = 0.3126

The degrees of freedom (DF) is:

DF = (s1²/n1 + s2²/n2)² / { [ (s1² / n1)² / (n1 - 1) ] + [ (s2² / n2)² / (n2 - 1) ] }

= (0.8²/29 + 1.1²/16)² / { [ (0.8² / 29)² / (29 - 1) ] + [ (1.1² / 16)² / (16 - 1) ] }

= 24 (Rounded to nearest integer)

Test statistic, t = Difference in means / SE = (4 - 5) / 0.3126 = -3.2

Part E

For two tail test, P-value = 2 * Pr[t < -3.2] = 2 * 0.0019 = 0.0038
The P-value in the problem is the probability of observing a sample statistic that is at least as extreme as your sample statistic when we assume that the null hypothesis is true (difference in average courses inmale and females is 0).

Part G

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
$\alpha$ = 0.05

(ii) Decision:

1.reject the null hypothesis

(iii) Reason for decision:

2.Since p-value < $\alpha$ , we reject the null hypothesis.   

(iv) Conclusion:

1.There is sufficient evidence to show that the mean number of English courses that males and females take is different.

part H choose choice 1 2 3 4

Explain how you determined which distribution to use.

2. The t-distribution will be used because the samples are independent and the population standard deviation is not known.