Steps for Hypothesis Testing in general a) State the null and alternative hypoth

Question

Steps for Hypothesis Testing in general a) State the null and alternative hypothesis. b) Select the distribution to use. c) Write the decision rule. (Define the rejection region.) d) Calculate the test statistic. e) Calculate the p-value. f) Make a decision. g) (Additional step for this worksheet) State the type I and II error in context of the problem 1. It has been reported that the average credit card debt for college seniors at the college book store for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995 with a standard deviation is $1100. With an alpha = 0.01, is the student senate correct? The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of 2.98 minutes in length. At an alpha = 0.05 can it be concluded that the average differs from the population average? Assume that the population is approximately normally distributed with a standard deviation of 0.98 minute. The percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large university health system, 5 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.10 level of significance to conclude that the proportion women physicians at the university health system exceeds of 27.9%?

Explanation / Answer

1) Claim : The average credit card debt less than $3264

So null hypothesis H0 : mu = 3264

Alternative hypothesis H1 : mu < 3264

n = 50, sample mean = x bar = 2995

Sample standard deviation = s = 1100

Since we are given sample standard deviation and sample size > 30 so we can use t test (that is we use t distribution) .

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis.

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here we need to use one sample left t test (because alternative hypothesis include < inequality)

Let me upload minitab output

Test of mu = 3264 vs < 3264

N Mean StDev SE Mean T P
50 2995 1100 156 -1.73 0.045

Test statistic value = t = -1.73

p-value = 0.045

Decision : We fail to reject null hypothesis at 1% of level of significance because p -value > 0.01

Type I error means reject null hypothesis if it is true

Type II error means reject alternative hypothesis when it is true (that is fail to reject wrong null hypothesis)

Type one error = here we fail to reject null hypothesis so there was no chance of type one error

There was chance of making type two error which is we say that the average credit card debt less than $3264 but in actual it is less than $3264 at 1% level of significance.

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