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Answer:
a. The margin of error is 2.29.
b. 19.23 to 23.81
Step-by-step explanation:
The sample size is n=64.
We start by calculating the sample mean and standard deviation with the following formulas:
The sample mean is M=21.52.
The sample standard deviation is s=6.89.
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
The t-value for a 99% confidence interval and 63 degrees of freedom is t=2.656.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
LL=M-t \cdot s_M = 21.52-2.29=19.23\\\\UL=M+t \cdot s_M = 21.52+2.29=23.81
The 99% confidence interval for the mean is (19.23, 23.81).
Answer:
a) There is suggestive evidence the velvet leaf seed is successful at weed control.
b) Lower bound: 3.699 Upper bound: 6.629
c) Since the confidence interval contains the average percent of seeds to be infected by the beetle (5.164), so we fail to reject the null hypothesis at the specified level of significance.
Step-by-step explanation:
See attached picture.
