# Question

The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies during 2007, both of which were conducted by Harris Interactive. In one of the studies,1001 adults were interviewed by telephone and asked about their hand-washing habits. In the other study, the hand-washing behavior of 6076 adults was inconspicuously observed within public rest rooms in four U.S. cities.

(a) In the telephone interviews, 921 of the adults said they always wash their hands in public rest rooms. Use this result to obtain a point estimate for the proportion of adults who say they always wash their hands in public rest rooms.

(b) Verify that the requirements for constructing a conﬁdence interval for p from part (a) are satisﬁed.

(c) Using the results from the telephone interviews, construct a 95% conﬁdence interval for the proportion of adults who say they always wash their hands in public rest rooms.

(d) Is it possible that the proportion of adults who say they always wash their hands in public rest rooms is less than 0.85? Is this likely?

(e) In the observational study, 4679 of the 6076 adults were observed washing their hands. Use this result to obtain a point estimate for the proportion of adults who wash their hands in public rest rooms.

(f) Verify that the requirements for constructing a conﬁdence interval for p from part (e) are satisﬁed.

(g) Using the results from the observational study, construct a 95% conﬁdence interval for the proportion of adults who wash their hands in public rest rooms.

(h) Is it possible that the proportion of adults who wash their hands in public rest rooms is greater than 0.85? Is this likely?

(i) Based on your ﬁndings in parts (a) through (h), what might you conclude about the proportion of adults who say they always wash their hands versus the proportion of adults who actually wash their hands in public rest rooms? Why do you think this is?

(a) In the telephone interviews, 921 of the adults said they always wash their hands in public rest rooms. Use this result to obtain a point estimate for the proportion of adults who say they always wash their hands in public rest rooms.

(b) Verify that the requirements for constructing a conﬁdence interval for p from part (a) are satisﬁed.

(c) Using the results from the telephone interviews, construct a 95% conﬁdence interval for the proportion of adults who say they always wash their hands in public rest rooms.

(d) Is it possible that the proportion of adults who say they always wash their hands in public rest rooms is less than 0.85? Is this likely?

(e) In the observational study, 4679 of the 6076 adults were observed washing their hands. Use this result to obtain a point estimate for the proportion of adults who wash their hands in public rest rooms.

(f) Verify that the requirements for constructing a conﬁdence interval for p from part (e) are satisﬁed.

(g) Using the results from the observational study, construct a 95% conﬁdence interval for the proportion of adults who wash their hands in public rest rooms.

(h) Is it possible that the proportion of adults who wash their hands in public rest rooms is greater than 0.85? Is this likely?

(i) Based on your ﬁndings in parts (a) through (h), what might you conclude about the proportion of adults who say they always wash their hands versus the proportion of adults who actually wash their hands in public rest rooms? Why do you think this is?

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