the critical value(s) for a left-tailed hypothesis test for a mean with the given characteristics. Round any z-value solution to two decimal places. Round any t-value solution to four decimal places.

• The significance level of the test is 2.5%
• The sample size is 65
• The population standard deviation () is not known

Should the t or z distribution be used for the above scenario?

• The standard normal (z) distribution should be used
• The Student's t distribution should be used

The critical value(s) for the test are given by ? z t =

According to a report published five years ago by the National Center for Education Statistics, the average time required to complete a bachelor's degree is 50 months. A researcher suspects that the it now takes students longer than 50 months, on average, to complete a bachelor's degree. A recent, random sample of 202 recent college graduates revealed that the average time to complete a bachelor's degree was 50.7 months, with a standard deviation of 7.8 months. Using =0.05, is there sufficient evidence to conclude that the average time required to complete a bachelor's degree is greater than 50 months? Use the p-value method. the null and alternative hypothesis for this test.

H0:H0:? = > < p = p p p p > p < H1:H1:? = > < p = p p p p > p < Determine if this test is left-tailed, right-tailed, or two-tailed.

• right-tailed
• two-tailed
• left-tailed

Should the standard normal (z) distribution or Student's (t) distribution be used for this test?

• The Student's t distribution should be used
• The standard normal (z) distribution should be used

the test statistic for the hypothesis test. Round the solution to four decimal places. the p-value (range) for the hypothesis test.

• p-value < 0.0005
• 0.0005 < p-value < 0.005
• 0.005 < p-value < 0.01
• 0.01 < p-value < 0.025
• 0.025 < p-value < 0.05
• 0.05 < p-value < 0.10
• p-value > 0.10

the appropriate conclusion for this hypothesis test.

• The sample data provide sufficient evidence to reject the null hypothesis that the average time required to complete a bachelor's degree is 50 months and thus we conclude that the average time required to complete a bachelor's degree is likely greater than 50 months.
• The sample data do not provide sufficient evidence to reject the null hypothesis that the average time required to complete a bachelor's degree is 50 months and thus we conclude that the average time required to complete a bachelor's degree is likely 50 months, as claimed.
• The sample data provide sufficient evidence to reject the alternative hypothesis that the average time required to complete a bachelor's degree is greater than 50 months and thus we conclude that the average time required to complete a bachelor's degree is likely 50 months, as claimed.
• The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average time required to complete a bachelor's degree is greater than 50 months and thus we conclude that the average time required to complete a bachelor's degree is likely greater than 50 months.