1) A luxury retailer requires that customers receive personal attention from sal

Question

1)

A luxury retailer requires that customers receive personal attention from sales associates within 5 min of entering a store. To test for adherence to policy, an analyst from the corporate office defined a null hypothesis, H0:=5 min, reflecting company policy on customer wait times, and formulated an alternative hypothesis, H1:>5 min, to indicate that customer wait times exceeded 5 min, on average.

A sample of 10 customers’ wait times revealed a sample standard deviation of 1.75 min. The analyst collected data for this sample at regular intervals, and experience has shown that this procedure gives data that can be treated as random samples from a normal population. Because of the small sample size, the analyst chose to use a one-sample ttest.

Determine the minimum value for mean wait time which, if observed in the sample, would lead the analyst to reject the null hypothesis at an alpha level of 0.05. Report results in minutes to three decimal places.

Minimum mean wait time required to reject the null hypothesis = ( )min?

2)

A biologist treated a field of tomato seedlings with an experimental pesticide. She was concerned that this new chemical might reduce the average height of treated plants below that of the species average of 30 in.

At harvest time, the biologist defined a null hypothesis, H0:=30 in, to reflect the species average height, and she formulated an alternative hypothesis, H1:<30 in, to indicate that the pesticide resulted in shorter plants, on average. She then collected a simple random sample of 20 mature plants from the experimental pesticide field, and measured the height of each plant. The standard deviation of the sample was 4 in. Experience has shown that these data can be treated as random samples from a normal population. Because of the small sample size, the biologist chose to test her hypothesis using a one-sample ttest.

Determine the maximum value of mean tomato plant height, which, if observed in the sample, would lead the biologist to reject the null hypothesis at an alpha level of 0.05. Report the result in inches, precise to three decimal places.

Maximum mean plant height required to reject the null hypothesis = ( ) in??

Explanation / Answer

1. the minimum wait time required to reject the null hypothesis is nothing but the population mean under H0+(s*critical value for the test)/sqrt(n) n =sample size s=sample sd

we are using a one sample t test with sample size=10 sample sd=1.75 population mean under H0=5

hence df=n-1=9

level of significance=alpha=0.05

alternative hypothesis is more than type.

hence the required value is t0.05;9 , the upper 0.05 point of a t distribution with df=9

using R t0.05;9=1.833113

hence the required Minimum mean wait time required to reject the null hypothesis

is 5+1.5*1.833113/sqrt(10)=5.86952 min [answer]

2. Maximum mean plant height required to reject the null hypothesis is population mean under H0+sample sd*critical value/sqrt(n) n=sample size

sample sd=4 sample size=n=20

population mean under H0:30

since one sample t test is used and alternative hypothesis is left sided and level of significance=0.05

so critical value =-t0.05:20-1=the lower 0.05 point of a t distribution with df=19= 1.729133

so the Maximum mean plant height required to reject the null hypothesis is 30-1.729133*4/sqrt(20)=28.4534 inch [answer]

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