One Sample Z Test

Here is the Question: Northwest Vista Collegeclaims that the students' mean scores in the Business programs are greater than 92 with a standard deviation of 15. A sample of 84 students is selected, and the mean score is 87. At 95% confidence level, is there enough evidence to support the claim? Fill in the information below to answer the question:

Step 1: Write the null and alternative hypothesis-

• Null hypothesis:
• Alternative hypothesis:

Step 2: Select appropriate statistic- Since the claim is student marks are greater than 92 marks; it is a right-tailed test.

Step 3: Determine the Level of significance: =

Step 4: Find the critical value: 1-=

Step 5: Look at the 0.95 in z table(Located online or in the appendix in the text)=

Step 6:Calculate the test statistics

• x =
• =
• =
• n =

Step 7: Interpret the results:

Compare Z_calcto Z_critical. In hypothesis testing, a critical value is a point on the test distribution compares to the test statistic to determine whether to reject the null hypothesis. If zcal value is greater than z critical value and it is in the rejection region. If so, we can reject the null hypothesis.

Step 8: State one or the other based on your test:

There is enough evidence to support the students' scores in their Business programs is greater than the 92 marks.

There is not enough evidence to support the students' scores in their Business programs is greater than the 92 marks.