In: Math
A study conducted by Stanford researchers asked children in two elementary schools in San Jose, CA to keep track of how much television they watch per week. The sample consisted of 198 children. The mean time spent watching television per week in the sample was 15.41 hours with a standard deviation of 14.16 hours.
(a) Carry out a one-sample t-test to determine whether there is convincing evidence that average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week. (Report the hypotheses, test statistic, p-value, and conclusion at the 0.10 level of significance.)
(b) Calculate and interpret a one-sample 90% t-confidence interval for the population mean.
(c) Comment on whether the technical conditions for the t-procedures are satisfied here. [Hint: What can you say based on the summary statistics provided about the likely shape of the population?]
a) H0: = 14
H1: > 14
The test statistic t = ()/(s/)
= (15.41 - 14)/(14.16/)
= 1.40
P-value = P(T > 1.40)
= 1 - P(T < 1.40)
= 1 - 0.9185
= 0.0815
Since the P-value is less than the significance level(0.0815 < 0.10), so we should reject the null hypothesis.
So there is sufficient evidence to support the claim that the average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week.
b) At 90% confidence interval the critical value is t* = 1.653
The 90% confidence interval is
+/- t* * s/
= 15.41 +/- 1.653 * 14.16/
= 15.41 +/- 1.66
= 13.75, 17.07
c) Since the population standard deviation is unknown, so we should use t-distribution.