Testing a claim about a population mean: t-Test

An overly involved "neighborhood watch" group has been investigating the length of lawns. In years past, lawns had been mowed to a mean length of 3.3 inches. A recent random sample of lawn lengths is given below. Conduct an appropriate test, at a 5% significance level, to determine if the overall mean lawn length is now higher than 3.3 inches.

Data (lawn lengths, measured in inches):

2.85
3.63
3.01
3.86
3.41
3.56
3.22
3.65
2.80
4.11
3.40
3.35
3.76
3.35
3.78
3.26

Checksum: 55

1. Consider the parameter of interest and choose the correct alternate hypothesis.
   
   • $\displaystyle \mu={3.3}$
   • $\displaystyle \mu\ge{3.3}$
   • $\displaystyle \mu>{3.3}$
   • $\displaystyle \mu\ne{3.3}$
   • $\displaystyle \mu\le{3.3}$
   • $\displaystyle \mu<{3.3}$
2. Are the necessary conditions present to carry out this inference procedure? Explain in context.
   
   • No. The sample is not large enough and the histogram is uniform.
   • Our sample was not larger than 30 in size, but a histogram has a reasonably symmetric bell shape. It is stated that the sample was randomly gathered. We assume that this is a small sample from a large population of lawns (that there are at least 10*16 lawns).

Carry out the procedure ("crunch the numbers"):

3. Sample mean: $\displaystyle \overline{{x}}\approx$
4. Standard deviation of the sample: $\displaystyle {s}\approx$
5. Standard error of sample mean: $\displaystyle \sigma_{\overline{{x}}}\approx$ Preview Question 6 Part 5 of 9  
6. Standardized test statistic: $\displaystyle {t}\approx$
7. P-value:
   

8. Decision:
   
   • Fail to reject the null hypothesis.
   • Reject the null hypothesis.
9. Write a conclusion in context.
   
   • Because our p-value (0.07542) is less than our level of significance (alpha=0.05), we have sufficient evidence to reject the null hypothesis. The evidence seems to indicate that the overall mean lawn lengthis higher than 3.3 inches.
   • Because our p-value (0.07542) is not less than our level of significance (alpha=0.05), we do not have sufficient evidence to reject the null hypothesis. We cannot conclude that the overall mean lawn length is higher than 3.3 inches.