Question

A Type 1 error is defined as:

• Rejecting a False Null Hypothesis
• Rejecting a True Null Hypothesis
• Failing to Reject a False Null Hypothesis
• Failing to Reject a True Null Hypothesis

b.) The probability for which a Type 1 error may occur in a hypothesis test is referred to as:

• Z-value
• Test Statistic
• Critical Value
• Level of Significance

c.) A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = -2.40. Assuming that the researcher is using a two-tailed test, what is the correct statistical decision?

• The researcher should reject the null hypothesis with either αα = 0.05 or αα = 0.01
• The researcher should reject the null hypothesis with αα = 0.05 but not with αα = 0.01
• The researcher should fail to reject the null hypothesis with either αα = 0.05 or αα = 0.01
• The researcher should fail to reject the null hypothesis with αα = 0.05 but not with αα = 0.01

d.) A hypothesis test produces a t statistic of t = 2.30. If the researcher is using a two-tailed test with αα = 0.05 How large does the sample size have to be to reject the null hypothesis?

• at least n = 8
• at least n = 9
• at least n = 10
• at least n = 11

e.) Which of the following situations is the most ideal for a researcher to perform a hypothesis test using the Standard Normal distribution as his/her Sampling Distribution.

• σσ is unknown; the population is normal; sample size = 20
• σσ is known; the population is not normal; sample size = 20
• σσ is unknown; the population is normal; sample size = 40
• σσ is known; the population is normal; sample size = 40

Answer 1

A) Type I error is defined as:

Rejecting a True null hypothesis.

B) The probability for which a Type 1 error may occur in a hypothestical test ts referred to as:

  Level of significance.

C) test statistic, z= -2.40

For = 0.05, crtical value= +- 1.96; That means that Reject the null hypothesis as test statistic lie in the critical region

For = 0.01, Critical value= +-2.5758, That means that Fail to reject the null hypothesis as the test statistic doe not lie in the critical region

   Answer- The researcher should reject the null hypothesis with =0.05 but not with =0.01

D) test statistic, t= 2.30

to reject the null hypothesis , critical value should be less than the test statistic

And for 0.025 ( ie. 0.05/2 as this is a two tail test) the crtical value just less than 2.30 is 2.262 corresponding to 9 degree of freedom

Now, Degree of freedom = n-1

S0. n= 10

Answer- at least n= 10

E) is known; the population is normal ;sample size is 40.