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Answer:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.
Step-by-step explanation:
Jenna claims that the average time of texting at her larger high school is greater than 94 minutes per day.
From here we can see that we have to perform a hypothesis test about a sample mean. The null and alternate hypothesis will be:
Null Hypothesis:
Alternate Hypothesis:
Jenna collected data from a sample of 32 students. So, sample size will be:
Sample Size = n = 32
Sample Mean = x = 96.5
Sample Standard Deviation = s = 6.3
We have to perform a hypothesis test, to test Jenna's claim. Since, the value of Population Standard Deviation is unknown and the value of Sample Standard Deviation is known, we will use One Sample t-test in this case.
The formula to calculate the test statistic is:
Using the values, we get:
The degrees of freedom will be:
df = n - 1 = 32 - 1 = 31
We have to convert the t-score 2.245 with 31 degrees of freedom to its equivalent p-value. From t-table this value comes out to be:
p-value = 0.0160
The significance level is:
Since, the p-value is lesser than the level of significance, we reject the Null Hypothesis.
Conclusion:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.